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- W2949590809 abstract "Let ${mathcal{K}}$ and ${mathcal{H}}$ be two Hilbert space, and let $B({mathcal{K}},{mathcal{H}})$ be the algebra of all bounded linear operators from ${mathcal{K}}$ into ${mathcal{H}}$. We say that an element $Gin B({mathcal{H}},{mathcal{H}})$ is an all-derivable point in $B({mathcal{H}},{mathcal{H}})$ if every derivable linear mapping $varphi$ at $G$ (i.e. $varphi(ST)=varphi(S)T+Svarphi(T)$ for any $S,Tin B(H)$ with $ST=G$) is a derivation. Let both $varphi: B({mathcal{H}},{mathcal{K}})rightarrow B({mathcal{H}},{mathcal{K}})$ and $psi: B({mathcal{K}},{mathcal{H}})rightarrow B({mathcal{K}},{mathcal{H}})$ be two linear mappings. In this paper, the following results will be proved : if $Yvarphi(W)=psi(Y)W$ for any $Yin B({mathcal{K}},{mathcal{H}})$ and $Win B({mathcal{H}},{mathcal{K}})$, then $varphi(W)=DW$ and $psi(Y)=YD$ for some $Din B({mathcal{K}})$. As an important application, we will show that an operator $G$ is an all-derivable point in $B({mathcal{H}},{mathcal{H}})$ if and only if $Gneq 0$." @default.
- W2949590809 created "2019-06-27" @default.
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- W2949590809 date "2014-05-17" @default.
- W2949590809 modified "2023-10-16" @default.
- W2949590809 title "Characterizations of all-derivable points in $B(H)$" @default.
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- W2949590809 doi "https://doi.org/10.48550/arxiv.1405.4455" @default.
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