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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Characterizations of all-derivable points in nest algebras


Authors: Jun Zhu and Sha Zhao
Journal: Proc. Amer. Math. Soc. 141 (2013), 2343-2350
MSC (2010): Primary 47L35, 47B47
Published electronically: March 6, 2013
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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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Additional Information

Jun Zhu
Affiliation: Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, People’s Republic of China
Email: junzhu@yahoo.cn

Sha Zhao
Affiliation: Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11511-X
PII: S 0002-9939(2013)11511-X
Keywords: All-derivable point, nest algebra, derivable linear mapping at $G$
Received by editor(s): April 24, 2010
Received by editor(s) in revised form: January 6, 2011, and October 13, 2011
Published electronically: March 6, 2013
Additional Notes: This work is supported by the National Natural Science Foundation of China (No. 10771191)
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society