Characterizations of all-derivable points in nest algebras

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 $G\ne 0$.

8 pages