O'SCANNLAIN, Circuit Judge.

In this case, we deal with the interplay between federal and state courts in a bitter and protracted dispute involving the enforcement of an arbitration award.

I

In January 1992, Stuart and Irene Wilson entered into a written agreement in California with Arrowhead Oil Corporation ("AOC") for the sale of certain franchise rights for the ownership and operation of a car care service business to be opened in Hawaii. AOC was a Lake Arrowhead, California-based regional sub-franchisor of SpeeDee Oil Change Systems ("SpeeDee"), a Louisiana Corporation, and in due course, the Wilsons opened their SpeeDee franchise, SpeeDee Oil of Maui, Inc, in Kahului, Hawaii. In 1993, AOC filed for bankruptcy, and SpeeDee took over the regional sub-franchise.

In 1994, the California Department of Corporations, after receiving complaints of unfair and deceptive sales practices (not necessarily related to this litigation), filed suit against SpeeDee and AOC. The state alleged that SpeeDee and AOC failed to disclose material facts in their Uniform Franchise Offering Circular, and made material misrepresentations with regard to franchise offerings, in violation of California securities law. In 1997, a California court entered judgment against SpeeDee and AOC, enjoining them from further sales in violation of state law. Subsequently, SpeeDee assigned its franchisor rights to G.C. K.B. Investments, Inc. ("GCKB"), also a Louisiana corporation.

SpeeDee's form franchise agreement contained an arbitration clause, requiring the franchisee to submit any claim or dispute arising under the agreement to binding arbitration. The agreement provided that arbitration was to be the sole dispute resolution method, and was to be conducted pursuant to the rules of the American Arbitration Association ("AAA"). The arbitration clause called for arbitration at the AAA office "located nearest the office of the[franchisor's] Region." The agreement also provided that litigation "to enforce any arbitration award . . . shall be held in San Bernardino County, California, or the federal court located nearest thereto."

The Wilsons allege that in the years following the opening of their franchise in Hawaii, SpeeDee repeatedly reneged on oral promises to the Wilsons to provide corporate support. As a result, the Wilsons stopped paying royalties and advertising funds due, and stopped reporting sales and related information to GCKB. GCKB filed with the AAA a demand for arbitration, which was set for February 9, 2000, in New Orleans, Louisiana, and the Wilsons were served with notice of the proceedings in accordance with AAA procedures. The Wilsons read the franchise agreement to require arbitration in California, not Louisiana. Objecting to the Louisiana arbitration on that basis, they refused to participate.

While the Wilsons chose not to make an appearance in the Louisiana arbitration, they did make various attempts to prevent the arbitration from going forward. First, they filed a motion to enjoin the arbitration in the ongoing litigation between the California Department of Corporations against SpeeDee and AOC for violations of state franchise law, but that motion was denied. Second, the Wilsons filed suit in Hawaii state court, seeking relief from the franchise agreement. The Hawaii court denied the Wilsons' application for a temporary restraining order, and denied their motion for a preliminary injunction.

The Wilsons' attempts to prevent the arbitration from going forward having failed, the Louisiana arbitrator, in February, 2000, granted an award in favor of GC KB on its claim. GC KB then, on March 14, 2000, filed an application for an order confirming its arbitration award in United States District Court for the Central District of California, pursuant to the arbitration agreement and to the Federal Arbitration Act ("FAA"). See 9 U.S.C. § 9. The Wilsons opposed, claiming that the California courts had already determined the agreement was illegal, and hence the arbitration award was invalid. On August 14, 2000, the federal district court confirmed the award, and the Wilsons timely appealed.

The Hawaii state courts issued two orders that would form the basis for a subsequent attack on the federal court's confirmation of the arbitration award in favor of GC KB. The first of these was issued on June 27, 2000, forty-seven days prior to the federal court's judgment confirming the Louisiana arbitration award, and was issued in response to a motion filed by GC KB requesting dismissal, or alternatively to compel arbitration, of the Wilsons' second amended complaint in the Hawaii litigation. The Hawaii court denied the motion to dismiss, but granted the motion to compel arbitration. The Hawaii court, however, read the agreement to provide for arbitration of those claims in California, not Louisiana, and so ordered.

The second arose out of GC KB's attempt to enforce its federal court judgment against the Wilsons in Hawaii state court, which enjoined such proceedings in an October 18, 2000 order because it found that such request was inconsistent with the order of arbitration entered June 27, 2000.

Armed with these two Hawaii state court orders, the Wilsons filed a "motion for limited remand" in district court, so that the district court might consider a Rule 60(b) motion. The Wilsons claimed that, taken together, the June and October orders issued in Hawaii invalidated the Louisiana arbitration award, hence rendering invalid the district court's entry of judgment on that award. The district court denied the motion, stating that the Hawaii court's October 18, 2000 order "does not decide that the arbitration award is either void or moot [but] merely temporarily enjoins [GC KB] from enforcing the award."

The Wilsons then went back to Hawaii state court and asked for an order "clarifying" its June 27, 2000 order, and urged it to find that the Louisiana arbitration was void and vacated. GC KB then sought an injunction in federal district court, seeking to prevent the Wilsons from interfering any further with its attempts to enforce its judgment, which was promptly granted in March, 2001. Notwithstanding the injunction, the Wilsons filed another post-judgment motion in district court, this time a Rule 60(b) motion for relief from judgment, essentially repeating the argument they made in their prior motion for limited remand.

In the meantime, the Hawaii state court duly issued its clarification order, holding that the federal district court had no subject matter jurisdiction over the dispute, and the Louisiana arbitration award was void and vacated. Thereafter, the federal district court denied the Wilsons' Rule 60(b) motion, and granted GC KB's motion for Rule 11 sanctions against the Wilsons and their attorneys.

In these consolidated appeals, the Wilsons timely challenge four decisions made by the district court: the confirmation of the arbitration award, the issuance of a permanent injunction, the denial of the Rule 60(b) motion, and the imposition of Rule 11 sanctions.

II

We first consider the Wilsons' challenge of the district court's entry of judgment confirming the default arbitration award.

A

The Wilsons assert that the Rooker-Feldman doctrine divested the district court of jurisdiction to enter judgment on the arbitration award. The Rooker-Feldman doctrine evolved from the Supreme Court's decisions in D.C. Court of Appeals v. Feldman, 460 U.S. 462, 103 S.Ct. 1303, 75 L.Ed.2d 206 (1983), and Rooker v. Fidelity Trust Co., 263 U.S. 413, 44 S.Ct. 149, 68 L.Ed. 362 (1923), and it rests on the principle that "a United States District Court has no authority to review final judgments of a state court in judicial proceedings." Feldman, 460 U.S. at 482, 103 S.Ct. 1303; Rooker, 263 U.S. at 416, 44 S.Ct. 149. The doctrine is not constitutionally based, but "arises out of a pair of negative inferences drawn from two statutes: 28 U.S.C. § 1331, which establishes the district court's original jurisdiction of all civil actions arising under the Constitution, laws, or treaties of the United States; and 28 U.S.C. § 1257, which allows Supreme Court review of final judgments or decrees rendered by the highest court of a State in which a decision could be had." In re Gruntz, 202 F.3d 1074, 1078 (9th Cir. 2000) (en banc) (internal quotations omitted); Dubinka v. Judges of the Sup. Ct. of the State of Cal. for the Co. of Los Angeles, 23 F.3d 218, 221 (9th Cir. 1994). While the language of 28 U.S.C. § 1257 applies only to final judgments of a state's highest court, we have previously held that the Rooker-Feldman doctrine applies to the decisions of lower state courts also, even those interlocutory in nature. Doe Associates v. Napolitano, 252 F.3d 1026, 1030 (9th Cir. 2001).

The Rooker-Feldman doctrine prohibits a federal district court from hearing two types of claims. First, a federal district court cannot engage in direct appellate review of state court determinations that have previously been adjudicated in any state court. Worldwide Church v. McNair, 805 F.2d 888, 890 (9th Cir. 1986) (federal district courts have "no authority to review the final determinations of a state court in judicial proceedings"). Second, a district court may not adjudicate claims that are "inextricably intertwined" with the merits of a judgment rendered in a state court proceeding. Feldman, 460 U.S. at 483 n. 16, 103 S.Ct. 1303. Were a district court to hear a claim that was inextricably intertwined with one previously decided in state court, "then the District Court is in essence being called upon to review the state court decision. This the District Court may not do." Id.

Courts have struggled with the contours of the "inextricably intertwined" prohibition, mostly in the context of constitutional challenges to state court action. We have said that the res judicata requirement of a full and fair opportunity to litigate, and the Feldman inextricably intertwined barrier are "two sides of the same coin." Robinson v. Ariyoshi, 753 F.2d 1468, 1472 (9th Cir. 1985), vacated on other grounds, 477 U.S. 902, 106 S.Ct. 3269, 91 L.Ed.2d 560 (1986).

Under the rubric of either jurisdiction or res judicata, the crux of the question is whether there has already been actual consideration of and a decision on the issue presented. If consideration and decision have been accomplished, action in federal court is an impermissible appeal from the state court decision. If no consideration has been given, or any decision on the matter is ambiguous, it is unlikely that the issues presented to the state high court and to the federal court are so inextricably intertwined that the federal court cannot take jurisdiction. Id. (citation and internal quotation marks omitted); see also McNair, 805 F.2d at 892 (following Robinson).

To be clear, the Wilsons do not claim that the district court lacked jurisdiction over the dispute when the petition to confirm the award was filed on March 14, 2000. The parties were diverse and an amount-in-controversy in excess of $75,000 was alleged, and hence the requirements of 28 U.S.C. § 1332 were satisfied. Rather, the Wilsons argue that the district court was divested of jurisdiction prior to the entry of its August 14, 2000 order reducing the arbitration award to judgment. This is so, they argue, because forty-seven days previously, the Hawaii state court had ordered arbitration to take place in California. That order, the argument goes, worked to divest the district court of jurisdiction a la Rooker-Feldman, because it "affected the rights of the parties" subject to the arbitration award and its subsequent confirmation.

This argument misconstrues the nature of a proceeding to confirm an arbitration award under the FAA. Section 9 of the FAA provides that a federal district court " must grant [a confirmation] order unless the award is vacated, modified, or corrected as prescribed in sections 10 and 11 of this title." 9 U.S.C. § 9 (emphasis added). There are only four grounds to vacate or to correct an arbitration award under sections 10 and 11: (1) fraud in the procurement of the agreement; (2) arbitrator corruption; (3) arbitrator misconduct or exceeding of powers; and (4) corrections for material miscalculations, exceeding of powers, or imperfection of form. Id. at §§ 10, 11. None of these grounds were at issue in the Hawaii state court decision of June 27, 2000. The district court therefore did not sit in "direct review" of the Hawaii state court.

The Wilsons argue that the two decisions are nonetheless "inextricably intertwined," contending that the district court based its judgment "on the grounds that [the Wilsons] signed an arbitration clause setting arbitration in Louisiana." They contend that there is a conflict with the Hawaii state court's June 27, 2000 determination that arbitration was to take place in California. However, this argument ignores the fact that the Hawaii state court ordered each party to arbitrate whatever claims were raised in the Wilsons' amended complaint filed in April, 2000, along with any claims or counterclaims of GC KB. That issue is entirely separate from the confirmability of the preexisting arbitration award. Further, the Hawaii state court ordered arbitration of whatever claims the Wilsons had against GC KB at GC KB's request. While the Wilsons would later try to use this order in an attempt to have the Louisiana arbitration voided altogether, it could hardly be plausibly argued that GC KB sought to rearbitrate issues already decided in its favor.

Rooker-Feldman does not apply here. The district court, in confirming GC KB's arbitration award, did not have to find that the Hawaii state court order was wrong. It simply dealt with the confirmability of the award pursuant to section 9 of the FAA, as opposed to the arbitrability of new claims raised in an amended complaint filed after the arbitration took place. There was no prohibited review of the Hawaii state court order and no collateral attack on any such judgment. The district court properly had jurisdiction to issue the order confirming the arbitration award.

B

The Wilsons also argue that the district court erred in entering judgment on the arbitration award because it failed to consider the legality of the underlying agreement pursuant to California law. They aver that, prior to entering judgment, the district court should have considered the California state court's holding that SpeeDee and AOC — GC KB's predecessors-in-interest — violated California securities laws in their offers and sales of SpeeDee franchises. The franchise agreement provided that the "legality of the offer and sale of the Franchise consummated hereby shall be governed by the applicable franchise investment law of the state in which the sale was made." The Wilsons conclude that the "law of California . . . applied to the Franchise agreement." Not to consider the legality of the sale and offer when reducing the arbitration award to judgment, they argue, constituted reversible error.

This proposition is incorrect as a matter of law. The FAA, while it does not itself create independent federal jurisdiction, "creates a body of federal substantive law establishing and regulating" arbitration agreements that come within the FAA's purview. Moses H. Cone Memorial Hospital v. Mercury Const. Corp., 460 U.S. 1, 25 n. 32, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983). The agreement at issue here is unquestionably one "evidencing a transaction involving commerce . . . or an agreement in writing to submit to arbitration an existing controversy arising out of such a contract." 9 U.S.C. § 2. Additionally, the franchise agreement contains a broad arbitration clause, whereby the Wilsons agreed to submit " any claim, dispute, suit, action or proceeding arising out of or relating to this Agreement . . . to binding arbitration." (emphasis added). Hence the FAA applies, not California law as the Wilsons urge.

As explained previously, the scope of a confirmation proceeding is extremely limited. Section 9 states that a district court " must grant such an order unless the award is vacated, modified, or corrected as prescribed in sections 10 and 11." 9 U.S.C. § 9. (emphasis added). Courts have interpreted sections 9 and 10 narrowly. "It is generally held that an arbitration award will not be set aside unless it evidences a manifest disregard for law." Todd Shipyards Corp. v. Cunard Line, 943 F.2d 1056, 1060 (9th Cir. 1991) (internal quotation marks omitted); Lapine Technology Corp. v. Kyocera Corp., 130 F.3d 884, 888 (9th Cir. 1997) ("It is beyond peradventure that . . . a federal court may vacate or modify an arbitration award only if that award is completely irrational, exhibits a manifest disregard of law, or otherwise falls within one of the grounds set forth in 9 U.S.C. §§ 10 or 11.") (internal quotation marks omitted). Confirmation of an arbitration award is required even in the face of erroneous misinterpretations of law. "It is not even enough that the [arbitrator] may have failed to understand or apply the law. An arbitrator's decision must be upheld unless it is completely irrational or it constitutes a manifest disregard of the law." French v. Merrill Lynch, 784 F.2d 902, 906 (9th Cir. 1986) (citations and internal quotation marks omitted); Todd Shipyards, 943 F.2d at 1060 (following French). But see Lapine 130 F.3d at 889 (federal courts can expand review of arbitration award beyond that allowed for in FAA, if, but only if, parties have contracted for expanded judicial review).

None of the limited grounds for vacating an arbitration award were put forth by the Wilsons, either to the district court or to this court on appeal. The Wilsons do not claim the award was procured by corruption, fraud or undue means, 9 U.S.C. § 10(a)(1), that the arbitrator was partial or corrupt, 9 U.S.C. § 10(a)(2), that the arbitrator refused to hear evidence or otherwise misbehaved, 9 U.S.C. § 10(a)(3), or that the arbitrator exceeded his powers, 9 U.S.C. § 10(a)(4). Nor do the Wilsons claim any mistake within the four corners of the award itself, such as a miscalculation of a sum or a misdescription of a person or thing, 9 U.S.C. § 11(a), or that the arbitrator acted on a matter not submitted to him, 9 U.S.C. § 11(b), or that there was a flaw in the form of the award, 9 U.S.C. § 11(c). Nor do the Wilsons stand on any of the judicially-developed grounds for vacating an award; that the award was irrational or involved a manifest disregard of the law.

The Wilsons' claim on appeal is essentially a belated attack on the legality of the agreement itself. The California state court had found that AOC and SpeeDee "failed to disclose material facts in their . . . offering circular . . . and made material oral misrepresentations with regard to the franchise offering," all in violation of California securities law. Contrary to the Wilsons' contention on appeal, however, the California court did not find that the franchise agreements themselves were illegal. The fact that GC KB's predecessors violated California securities laws with respect to the offer and sale of franchises is simply not a proper objection in a proceeding to confirm an arbitration award. To the extent those securities law violations comprise any sort of defense to the Wilsons' subsequent breach of the franchise agreement, they should have been raised with the arbitrator, and not before the district court in the subsequent confirmation proceeding.

To summarize, federal law governs the confirmability of an arbitration award. The scope of such a proceeding is strictly prescribed by statute and decisional law. The district court made no error in failing to consider the legality of the underlying agreement pursuant to California law.

III

Next, we consider the district court's entry of a permanent injunction against the Wilsons, enjoining them from pursuing any further the Hawaii litigation in an attempt to circumvent the enforcement of the district court's judgment.

A

First, the Wilsons contend the injunction issued by the district court violated the Anti-Injunction Act, 28 U.S.C. § 2283, because the district court acted "oppressively" in attempting to quash the Hawaii state court action. Whether an injunction may issue under the Anti-Injunction Act is a question of law reviewed de novo. California v. Randtron, 284 F.3d 969, 974 (9th Cir. 2002).

The Anti-Injunction Act prohibits a federal court from enjoining state court proceedings except where an injunction is "expressly authorized by Act of Congress, or where necessary in aid of its jurisdiction, or to protect or effectuate its judgments." 28 U.S.C. § 2283. In the interest of comity and federalism, the exceptions must be strictly construed. Golden v. Pacific Maritime Ass'n, 786 F.2d 1425, 1427 (9th Cir. 1986). "[D]oubts as to the propriety of a federal injunction against state court proceedings should be resolved in favor of permitting the state courts to proceed in an orderly fashion to finally determine the controversy." Atlantic Coast Line Railroad Co. v. Brotherhood of Locomotive Engineers, 398 U.S. 281, 297, 90 S.Ct. 1739, 26 L.Ed.2d 234 (1970).

The district court issued its injunction under the third of these exceptions, the `relitigation' exception. The relitigation exception was designed to permit a federal court to prevent state court litigation of an issue that was previously presented to and decided by a federal court. Chick Kam Choo v. Exxon Corp., 486 U.S. 140, 147, 108 S.Ct. 1684, 100 L.Ed.2d 127 (1988). A district court may properly issue an injunction under the relitigation exception if "there could be an actual conflict between the subsequent state court judgment and the prior federal judgment." Blalock Eddy Ranch v. MCI Telecomms. Corp., 982 F.2d 371, 375 (9th Cir. 1992). Even if no actual conflict is possible, an injunction "could still be proper if res judicata would bar the state court proceedings." Id.

Applying these principles to the present case, it is apparent the injunction falls within the permissible scope of the relitigation exception. After the district court entered judgment on the arbitration award in favor of GC KB, the Wilsons went back to Hawaii state court and asked it to find the Louisiana arbitration was "void, vacated, and of no force and effect." There was, therefore, an actual conflict — not just a possible one — between the federal court's entry of judgment on that award, and a request that the state court find the arbitration award was invalid. Blalock Eddy Ranch, 982 F.2d at 375. The Wilsons characterize their request as no more than an order seeking `clarification' of the Hawaii court's earlier order, but it was clearly an attempt to circumvent the enforcement of the district court's judgment in favor of GC KB. The district court was entitled to defend its judgment under the relitigation exception.

B

Next, the Wilsons claim that even if the Anti-Injunction Act was not violated, the district court nonetheless erred in entering injunctive relief against them. The requirements for the issuance of a permanent injunction are (1) the likelihood of substantial and immediate irreparable injury, and (2) the inadequacy of remedies at law. See LaDuke v. Nelson, 762 F.2d 1318, 1330 (9th Cir. 1985). The decision to grant or deny injunctive relief "rests within the sound discretion of the trial court and . . . will not be disturbed unless there has been a clear abuse of it." SEC v. Arthur Young Co., 590 F.2d 785, 787 (9th Cir. 1979) (citation and internal quotation marks omitted). A district court abuses its discretion when it rests its conclusions on clearly erroneous factual findings. Golden, 786 F.2d at 1426.

The district court enjoined the Wilsons from taking any action to interfere with GC KB's attempts to enforce its judgment against them, including taking any action to prosecute the Hawaii state court litigation, and pursuing the arbitration ordered by the Hawaii state court. The district court found that GC KB was faced with the likelihood of immediate and irreparable injury because it was "forced to relitigate [the same issue] a number of times, at its own expense, in various state court proceedings . . . and has not received royalties and other sums due, as determined by the arbitration proceedings." Unless the Wilsons were enjoined from seeking further relief, future injury was likely. The court also determined that GC KB had no adequate remedy at law to prevent the Wilsons from continuing to relitigate in Hawaii state court.

The Wilsons do not contend on appeal that in fact GC KB did not face irreparable injury, or that contrary to the district court's finding, GC KB had no adequate remedy at law. Rather they argue that the injunction was based on an erroneous reading of the franchise agreement, in that the district court incorrectly read the arbitration provision to require arbitration in Louisiana, when in fact the agreement called for arbitration in California. Thus, we come to the heart of the Wilsons' objection to the Louisiana arbitration.

The arbitration clause requires arbitration at the AAA office "located nearest to the office of the Region." The "Region" is defined in the fourth line of the agreement as the franchisor, AOC. "The Region" is used literally hundreds of times in the franchise agreement to refer to the franchisor. GC KB, a Louisiana corporation, is the successor-in-interest to AOC, and the Wilsons do not contend otherwise. GC KB, as the successor-in-interest to AOC, is "the Region" for purposes of the franchise agreement, and as such, it commenced arbitration proceedings in the AAA's New Orleans office; that is, the AAA office "located nearest to the office of the Region."

The Wilsons point to a provision of the agreement entitled "Notices," which references AOC's address in Lake Arrowhead Village, California, and the Wilsons' home address in Texas. The provision states that "[a]ll notices hereunder shall be . . . addressed to either party at the following addresses." This provision could not be clearer. As its title explicitly states, it is a notice provision, and not a venue provision as the Wilsons contend. Therefore, the district court did not base its decision to enjoin the Hawaii proceedings on an erroneous reading of the franchise agreement.

IV

The Wilsons next assert the district court erred in denying their Rule 60(b) motion for post-judgment relief. We review the denial of Rule 60(b) motion for an abuse of discretion. Community Dental Services v. Tani, 282 F.3d 1164, 1167 n. 7 (9th Cir. 2002); Bateman v. United States Postal Service, 231 F.3d 1220, 1223 (9th Cir. 2000).

The Wilsons based their request for post-judgment relief on the order of clarification issued by the Hawaii state court on April 30, 2001. That order found the "Louisiana Arbitration Award is void and vacated, effective as of the date of the filing of this Court's previous order, June 27, 2000." The Hawaii state court further found that the district court "has no subject matter jurisdiction over these proceedings." The Wilsons argue that because the arbitration award was void and vacated, so too was the federal district court's judgment entered on that award, and they were entitled to relief pursuant to Federal Rule of Civil Procedure 60(b)(4) and 60(b)(5).

This argument begs the question whether a state court can void a federal court decree nunc pro tunc. The well-established principle is to the contrary, for "[s]tate courts have no power to void federal court decrees," and "[a] federal court may enjoin such impermissible collateral attacks on federal judgments." Western Systems v. Ulloa, 958 F.2d 864, 868 (9th Cir. 1992) (state has no power to declare federal court order "null and void"); Williams Natural Gas Co. v. Oklahoma City, 890 F.2d 255, 264 (10th Cir. 1989) (finding error not to enjoin collateral attack by state court on the validity of federal judgment). If that were not enough, the motion was based on an order the Wilsons were properly enjoined from pursuing in the first place. The district court did not abuse its discretion in denying the motion for post-judgment relief.

V

Finally, the Wilsons challenge the imposition of Rule 11 sanctions. The district court's Rule 11 determination is reviewed for an abuse of discretion. Cooter Gell Co. v. Hartmarx Corp., 496 U.S. 384, 405, 110 S.Ct. 2447, 110 L.Ed.2d 359 (1990); Terran v. Kaplan, 109 F.3d 1428, 1434 (9th Cir. 1997).

Among other grounds, a district court may impose Rule 11 sanctions if a paper filed with the court is for an improper purpose, or if it is frivolous. Fed.R.Civ.Pro. 11(b)(1)-(2); Townsend v. Holman Consulting, 929 F.2d 1358, 1362 (9th Cir. 1990) (en banc). The standard governing both the "improper purpose" and "frivolous" inquiries is objective. Id. "[T]he subjective intent of the . . . movant to file a meritorious document is of no moment. The standard is reasonableness. The `reasonable man' against which conduct is tested is a competent attorney admitted to practice before the district court." Zaldivar v. City of Los Angeles, 780 F.2d 823, 830 (9th Cir. 1986).

In this case, the district court imposed monetary sanctions in the amount of $19,350, which the court determined was GC KB's reasonable attorneys fees for opposing the Wilsons' Rule 60(b) motion and their motion for reconsideration, and for seeking an injunction against the Wilsons' attempts to block the enforcement of judgment in Hawaii state court.

A

The district court found the Rule 60(b) motion for relief from judgment was a frivolous paper in violation of Rule 11(b)(2). Applying the Zaldivar objective reasonableness standard, the court held that "a competent attorney would not, in good faith, base a Motion for Relief on two state court orders that this Court enjoined him from seeking." The Wilsons correctly point out that one of these orders, the June 27, 2000 order, predated the district court's injunction, which was not entered until March 23, 2001. They characterize this assertion on the district court's part as a "clearly erroneous assessment of the evidence" and hence an abuse of the district court's discretion. Terran, 109 F.3d at 1434.

The Wilsons' argument is unpersuasive. The basis for the Wilsons' Rule 60(b) motion was the Hawaii state court order `clarifying' its earlier order and vacating the arbitration award. This order was issued after the injunction was entered, and after the district court had ruled that the Hawaii orders "did not constitute grounds for setting aside this Court's previously-entered order." The Wilsons had fair warning not to pursue the Hawaii litigation in an attempt to subvert the district court judgment. The district court did not award sanctions for failure to adhere to the injunction; rather, the sanctions were imposed because the Wilsons used the interim Hawaii court order in an attempt to gain post-judgment relief. Ultimately, the court found that no reasonable attorney would have based a Rule 60(b) motion on an order the party was enjoined from pursuing in the first place. Under the circumstances, we cannot say the district court abused its discretion in concluding that the Rule 60(b) motion was frivolous.

B

The district court also found that the Wilsons and their attorney filed papers for an "improper purpose" in violation of Rule 11(b)(1). As with frivolous pleadings, whether a paper is filed for an improper purpose is "tested by objective standards." Zaldivar, 780 F.2d at 831 n. 9. An improper purpose is a purpose to "harass or to cause unnecessary delay or needless increase in the cost of litigation." Fed.R.Civ.Pro. 11(b)(1). We have previously stated that "[w]ithout question, successive complaints based upon propositions of law previously rejected may constitute harassment under Rule 11." Zaldivar, 780 F.2d at 832; Buster v. Greisen, 104 F.3d 1186, 1190 (9th Cir. 1997).

The district court found that the Wilsons "filed successive motions based on propositions of law clearly rejected by the Court." G.C. K.B. Investments, Inc. v. Wilson, No. 00-00148-VAP (C.D.Cal. May 17, 2001) (order granting motion for monetary sanctions). The filings "failed to allege anything other than the same argument repeatedly rejected by this Court: that a state court in Hawaii can prevent or invalidate this Court's affirmation of an arbitration award." Id. An examination of the successive motions filed in federal court by the Wilsons supports the district court's conclusion. In their opposition to the confirmation request, their motion for limited remand, their motion for relief from judgment, and their opposition to the request for an injunction, the Wilsons repeat the same argument: arbitration was improper in Louisiana, and the Hawaii state court proceedings trump the proceedings in federal district court. The district court properly applied the Zaldivar standard for harassment, and did not abuse its discretion in concluding that the filings were made for an improper purpose.

AFFIRMED.