Characterizations of Jordan derivations on strongly double triangle subspace lattice algebras

Authors

  • jiankui li

Keywords:

Derivation, Jordan derivation, subspace lattice

Abstract

Let $\mathcal{D}$ be a strongly double triangle subspace lattice on a complex reflexive Banach space $X$ and let $\delta:\mathrm{Alg}\mathcal{D}\rightarrow \mathrm{Alg}\mathcal{D}$ be a linear mapping. We show that $\delta$ is Jordan derivable at zero point, i.e., $\delta(AB+BA)=\delta(A)B+A\delta(B)+\delta(B)A+B\delta(A)$ whenever $AB+BA=0$ if and only if $\delta$ has the form $\delta(A)=\tau(A)+\lambda A$ for some derivation $\tau$ and some scalar $\lambda$. We also show that if the dimension of $X$ is greater than 2, then $\delta$ satisfies $\delta(AB+BA)=\delta(A)B+A\delta(B)+\delta(B)A+B\delta(A)$ whenever $AB=0$ if and only if $\delta$ is a derivation.

Published

2011-10-19

Issue

Vol. 84 No. 2 (2011)

Section

Articles
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