Jordan τ-derivations of locally matrix rings
Journal
Algebras and Representation Theory
Journal Volume
16
Journal Issue
3
Pages
755-763
Date Issued
2013
Author(s)
Abstract
Let R be a prime, locally matrix ring of characteristic not 2 and let Q ms (R) be the maximal symmetric ring of quotients of R. Suppose that δ R\to Q (R) is a Jordan τ-derivation, where τ is an anti-automorphism of R. Then there exists a â̂̂ Q ms (R) such that δ(x) = xa - aτ(x) for all x â̂̂ R. Let X be a Banach space over the field {\mathbb F of real or complex numbers and let B(X) be the algebra of all bounded linear operators on X. We prove that Q (B)(X))={B}(X), which provides the viewpoint of ring theory for some results concerning derivations on the algebra {B}(X). In particular, all Jordan τ-derivations of {B}(X) are inner if F X>1. © 2011 Springer Science+Business Media B.V.
Type
journal article