Generalized derivations and additive theory II

Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (ii)

In this paper, we introduce and discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module.

Generalized Derivations on Modules

Applications of Cut-Free Infinitary Derivations to Generalized Recursion Theory

Cut elimination is the main tool in proof theoretical research. The emphasis there, however, is on the cut–elimination procedure, i.e., the dynamical aspect of cut–elimination. In this paper we want to show that also the statical aspect, i.e., the mere existence of cut–free derivations, has consequences which may be viewed to belong to Descriptive Set Theory or Generalized Recursion Theory. We ...

Generalized Derivations on Modules *

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 th...

Nearly Generalized Jordan Derivations

Let A be an algebra and let X be an A-bimodule. A C−linear mapping d : A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ : A → X such that d(a) = ad(a) + δ(a)a for all a ∈ A. The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.