Generalized Jordan derivation on nest algebras

Generalized sigma-derivation on Banach algebras

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

Jordan derivation on trivial extension

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

generalized sigma-derivation on banach algebras

let $mathcal{a}$ be a banach algebra and $mathcal{m}$ be a banach $mathcal{a}$-bimodule. we say that a linear mapping $delta:mathcal{a} rightarrow mathcal{m}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{a} rightarrow mathcal{m}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{a}$. giving some facts concerning general...

Additivity of Jordan Triple Product Homomorphisms on Generalized Matrix Algebras

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from Mn(A) (A is not necessarily a prime algebra) onto an arbitrary ring R is additive.