Can a federal judge exercise jurisdiction over a state official on a habeas petition?

Malone insists that Mitchum v. Foster, 407 U.S. 225, 92 S.Ct. 2151, 32 L.Ed.2d 705 (1972), created an exception to the Anti-Injunction Act for habeas petitions. On this basis, he argues, we may exercise jurisdiction over the Missouri officials. The Anti-Injunction Act prohibits federal courts from staying proceedings in state courts except when necessary to aid the court's jurisdiction or to protect or effectuate a judgment of the court. While the Anti-Injunction Act may not bar a federal court from granting injunctive relief in a habeas case, the Act does not create jurisdiction in cases where the petitioner would otherwise be without recourse.