Generalized skew derivations with nilpotent values on left ideals of rings and Banach algebras

Abstract

AbstractApplying the extended Jacobson density theorem for rings with automorphisms and skew derivations, we characterize a generalized skew derivation of rings or Banach algebras so that the values of on a left ideal are nilpotent. The analogous results for -algebras and standard operator algebras on Banach spaces are also described.Keywords: generalized skew derivationprime ringBanach algebraC*-algebrastandard operator algebraAMS Subject Classifications: 16W2547B4747B48 AcknowledgmentsThe authors would like to thank the referee for the very thorough reading of the paper and valuable comments. This research is supported by the NSC 100-2811-M-018-012 of Taiwan.