ORDER
Thomas Ducey and his defunct law firm, Ducey & Associates, appeal from an order imposing sanctions for filing a complaint duplicating litigation that an Illinois court *593already had referred to arbitration. We affirm the judgment.
The underlying events began nearly two decades ago and arose out of Ducey’s representation of Mac Copeland, a snack-food wholesaler in St. Clair County, Illinois. With Ducey as his attorney, Copeland filed suit in state court in 1993, claiming that Tom’s Foods, a Georgia manufacturer of snack foods, had authorized two other defendants to distribute the company’s products within the exclusive sales territory contractually guaranteed to him. In May 2002, the state court granted the defendants’ motion to compel arbitration and stayed proceedings until the completion of arbitration. Copeland filed a notice of appeal from that ruling, but Ducey failed to tender the record to the appellate court, leading to dismissal of the appeal in August 2002 for lack of prosecution.
Meanwhile, shortly before the state court ordered arbitration, Ducey had filed a complaint in federal court raising the same claims as in the state litigation. The district court dismissed the complaint for inadequate pleading of facts supporting diversity jurisdiction. Soon after that dismissal the state court issued its arbitration ruling, but instead of submitting the matter for arbitration or following through with the state-court appeal, Ducey refiled his federal complaint. Again the district court dismissed the complaint for inadequate pleading of diversity jurisdiction. Then in May 2004 — almost two years after Copeland’s appeal from the order compelling arbitration had been dismissed — Du-cey tried again in federal court. His complaint in this third federal action mirrors his state suit and the previous federal complaints. The defendants moved to dismiss the action or to stay the proceedings in light of the-state-court case. They principally argued that the state court’s decision compelling arbitration was preclusive. In the alternative, the defendants argued that the district court lacked subject-matter jurisdiction to review the state court’s decision under the Rooker-Feldman doctrine, see D.C. Court of Appeals v. Feldman, 460 U.S. 462, 103 S.Ct. 1303, 75 L.Ed.2d 206 (1983); Rooker v. Fidelity Trust Co., 263 U.S. 413, 44 S.Ct. 149, 68 L.Ed. 362 (1923), and that, if the district court did have jurisdiction, it should stay proceedings under Colorado River Water Conservation District v. United States, 424 U.S. 800, 96 S.Ct. 1236, 47 L.Ed.2d 483 (1976). Ducey never responded on Copeland’s behalf, leading the district court to treat the merits of the motion as admitted and dismiss the case. See S.D. Ill. R. 7.1(c).
In the same order, the district court sua sponte directed Ducey and his firm to show cause why they should not be sanctioned under Federal Rule of Civil Procedure 11(c) for filing the complaint. The order cited the provisions of Rule 11 that the judge believed Ducey had violated and noted that the complaint “duplicates a ten year old state court case and a case that was previously filed twice and dismissed twice in this district court.” Ducey’s response acknowledged that the federal litigation involved the “same parties and issues” as the state case. He told the court that he “did not file this action in this court for the purpose of harassment” but did not explain why he was filing duplica-tive litigation or why he was continuing to pursue Copeland’s claims in federal court after the state court had ordered them arbitrated. He explained that he failed to respond to the defendants’ motion to dismiss because his “computer system” had been struck by lightning, erasing his scheduling information.
The district court ordered Ducey and his law firm to pay the court $3,000 as a sanction. Noting that Ducey had admitted that Copeland’s federal and state suits *594were identical, the court found that the latest federal complaint had been filed for an improper reason and lacked a sufficient legal foundation. See Fed.R.Civ.P. 11(b)(1), (2).
Ducey and his firm have appealed from that ruling. Proceedings in this court were stayed for six years while Tom’s Foods went through bankruptcy proceedings, and the intervening years were not kind to Ducey. His law license has been suspended almost continuously since August 2005 for ethical violations, see Lawyer Search: Attorney’s Registration and Public Disciplinary Record for Cornelius Thomas Ducey, Jr., available at https:// www.iardc.org/ldetail.asp?id=73825600 (last visited Jan. 9, 2012), and his firm was dissolved in 2010, see Corporation File Detail Report for Ducey & Associates, P.C., available at http://www.ilsos.gov/ corporatellc/CorporateLlcController (search “Ducey & Associates, P.C.”) (last visited Jan. 9, 2012). The firm participates in this appeal under the Illinois statute allowing for post-dissolution actions. See 805 ILCS 5/12.80; Tamburo v. Dworkin, 601 F.3d 693, 698 n. 2 (7th Cir.2010). Du-cey also informs us that he suffered a stroke in 2006 following brain surgery and has been in speech therapy since. Ducey agrees, however, that with the bankruptcy proceedings now over, this appeal can proceed to disposition.
Ducey advances three arguments attacking the sanctions order, which we review for abuse of discretion. Matrix IV, Inc. v. Am. Nat’l Bank & Trust Co. of Chi., 649 F.3d 539, 552 (7th Cir.2011); Nemsky v. ConocoPhillips Co., 574 F.3d 859, 868 (7th Cir.2009). First, he contends that the district court gave him inadequate notice that he faced possible sanctions. Ducey is correct that a court contemplating sanctions sua sponte under Rule 11 must give the offending party notice of the allegedly sanctionable conduct and a chance to respond. See Fed.R.Civ.P. 11(c)(1), (3); Johnson v. Cherry, 422 F.3d 540, 551-52 (7th Cir.2005). The notice must specify the offending conduct, but only to the extent necessary to ensure that the party facing sanctions has an adequate chance to defend himself. See In re Rim-sat, Ltd., 212 F.3d 1039, 1046 (7th Cir. 2000); In re Taylor, 655 F.3d 274, 286-87 (3d Cir.2011); Clark v. United Parcel Serv., Inc., 460 F.3d 1004, 1008 (8th Cir. 2006). The district judge in this case complied with these requirements. He identified which filing (the complaint) was potentially sanctionable, laid out the provisions of Rule 11 that he believed Ducey had violated, and gave Ducey almost three weeks to respond. The show-cause order also noted that the federal complaint was a carbon copy of the state-court filing, which Ducey knew had been referred to arbitration. This was more than enough to put Ducey on notice of the need to explain his rationale and legal justification for filing the complaint.
Second, Ducey argues that the district court improperly sanctioned him for his state court filings, thereby exceeding the scope of Rule 11. See Bisciglia v. Kenosha Unified Sch. Dist. No. 1, 45 F.3d 223, 226-27 (7th Cir.1995); Schoenberger v. Oselka, 909 F.2d 1086, 1087 (7th Cir. 1990). But this contention is baseless. The district court sanctioned Ducey for filing a complaint in federal court for improper reasons and without sufficient legal support. See Fed.R.CivP. 11(b)(1), (2).
Finally, Ducey contends that the district court lacked adequate legal basis to sanction him. He notes correctly that federal courts may, as a general matter, entertain suits parallel to actions ongoing in state court. Exxon Mobil Corp. v. Saudi Basic Indus. Corp., 544 U.S. 280, 292, 125 S.Ct. 1517, 161 L.Ed.2d 454 (2005); *595TruServ Corp. v. Flegles, Inc., 419 F.3d 584, 590 (7th Cir.2005). But a court acts well within its discretion when it imposes Rule 11 sanctions for filing claims that already have been resolved in prior litigation. See Bethesda Lutheran Homes & Servs., Inc. v. Born, 238 F.3d 853, 859 (7th Cir.2001); Hapaniewski v. City of Chicago Heights, 883 F.2d 576, 580-81 (7th Cir. 1989); Cannon v. Loyola Univ. of Chi., 784 F.2d 777, 782 (7th Cir.1986); Kountze ex rel. Gilbert M. and Martha H. Hitchcock Found. v. Gaines, 536 F.3d 813, 819 (8th Cir.2008). In this case, although Copeland had the option of waiting to appeal the order compelling arbitration until after entry of a final judgment, see Salsitz v. Kreiss, 198 Ill.2d 1, 260 Ill.Dec. 541, 761 N.E.2d 724, 729-30 (2001), he chose instead to pursue his right to an interlocutory appeal, see id.; Fosier v. Midwest Care Center II, Inc., 398 Ill.App.3d 563, 340 Ill.Dec. 282, 928 N.E.2d 1, 6 (Ill.App. Ct.2010). The state court’s decision compelling arbitration thus became final in 2002, when Copeland’s interlocutory appeal was dismissed for lack of prosecution, and was entitled to preclusive effect. See John Crane, Inc. v. Admiral Ins. Co., 354 Ill.Dec. 201, 957 N.E.2d 517, 522-23 (Ill. App.Ct.2011); Woodson v. Chi Bd. of Educ., 154 Ill.2d 391, 182 Ill.Dec. 15, 609 N.E.2d 318, 320-21 (1993). We put to the side the subtleties of the Rooker-Feldman doctrine and Colorado River abstention and conclude that the district judge did not abuse his discretion in determining that this duplicative, issue-precluded suit was filed for an improper purpose and lacked an adequate legal foundation.
AFFIRMED.