Characterizations of all-derivable points in nest algebras

Zhu, Jun; Zhao, Sha

doi:10.1090/S0002-9939-2013-11511-X

Characterizations of all-derivable points in nest algebras
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by Jun Zhu and Sha Zhao PDF

Proc. Amer. Math. Soc. 141 (2013), 2343-2350 Request permission

Abstract:

Let $\mathcal {A}$ be an operator algebra on a Hilbert space. We say that an element $G\in {\mathcal {A}}$ is an all-derivable point of ${\mathcal {A}}$ if every derivable linear mapping $\varphi$ at $G$ (i.e. $\varphi (ST)=\varphi (S)T+S\varphi (T)$ for any $S,T\in alg{\mathcal {N}}$ with $ST=G$) is a derivation. Suppose that $\mathcal {N}$ is a nontrivial complete nest on a Hilbert space $H$. We show in this paper that $G\in {alg\mathcal {N}}$ is an all-derivable point if and only if $G\neq 0$.

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