Generalized Jordan N-Derivations of Unital Algebras with Idempotents

Characterization of Pseudo n-Jordan homomorphism Between unital algebras

Let A and B be Banach algebras and B be a right A-module. In this paper, under special hypotheses we prove that every pseudo (n+1)-Jordan homomorphism f:A----> B is a pseudo n-Jordan homomorphism and every pseudo n-Jordan homomorphism is an n-Jordan homomorphism

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

Jordan Derivations and Antiderivations of Generalized Matrix Algebras

Let G = [ A M N B ] be a generalized matrix algebra defined by the Morita context (A,B,A MB,B NA,ΦMN ,ΨNM) . In this article we mainly study the question of whether there exist the so-called “proper” Jordan derivations for the generalized matrix algebra G . It is shown that if one of the bilinear pairings ΦMN and ΨNM is nondegenerate, then every antiderivation of G is zero. Furthermore, if the ...

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.

Jordan ∗−homomorphisms between unital C∗−algebras

Let A,B be two unital C∗−algebras. We prove that every almost unital almost linear mapping h : A −→ B which satisfies h(3uy + 3yu) = h(3u)h(y) + h(y)h(3u) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, ..., is a Jordan homomorphism. Also, for a unital C∗−algebra A of real rank zero, every almost unital almost linear continuous mapping h : A −→ B is a Jordan homomorphism when h(3uy + 3yu) = h...