Generalized Derivations on Modules *
نویسنده
چکیده
Let A be a Banach algebra and M be a Banach left A-module. A linear map δ : M → M is called a generalized derivation if there exists a derivation d : A → A such that δ(ax) = aδ(x) + d(a)x (a ∈ A,x ∈ M). In this paper, we associate a triangular Banach algebra T to Banach A-module M and investigate the relation between generalized derivations on M and derivations on T . In particular, we prove that the so-called generalized first cohomology group of M is isomorphic to the first cohomology group of T .
منابع مشابه
Approximately Quasi Inner Generalized Dynamics on Modules
We investigate some properties of approximately quasi inner generalized dynamics and quasi approximately inner generalized derivations on modules. In particular, we prove that if A is a C*-algebra, is the generator of a generalized dynamics on an A-bimodule M satisfying and there exist two sequences of self adjoint elements in A such that for all in a core for , , then is approx...
متن کاملApproximately higher Hilbert $C^*$-module derivations
We show that higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.
متن کاملArens regularity and derivations of Hilbert modules with the certain product
Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$ is Arens regular. We also study the relationship between derivations of $A$ and $E$.
متن کاملOn the stability of generalized derivations on Banach algebras
We investigate the stability of generalizedderivations on Banach algebras with a bounded central approximateidentity. We show that every approximate generalized derivation inthe sense of Rassias, is an exact generalized derivation. Also thestability problem of generalized derivations on the faithful Banachalgebras is investigated.
متن کامل