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

 

Bilocal derivations
of standard operator algebras


Authors: Jun Zhu and Changping Xiong
Journal: Proc. Amer. Math. Soc. 125 (1997), 1367-1370
MSC (1991): Primary 47D30, 47D25, 47B47
MathSciNet review: 1363442
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Abstract: In this paper, we shall show the following two results: (1) Let $A$ be a standard operator algebra with $I$, if $\Phi $ is a linear mapping on $A$ which satisfies that $\Phi (T)$ maps $\ker T$ into $\operatorname {ran} T$ for all $T\in A$, then $\Phi $ is of the form $\Phi (T)=TA+BT$ for some $A,B$ in $B(X)$. (2) Let $X$ be a Hilbert space, if $\Phi $ is a norm-continuous linear mapping on $B(X)$ which satisfies that $\Phi (P)$ maps $\ker P$ into $\operatorname {ran} P$ for all self-adjoint projection $P$ in $B(X)$, then $\Phi $ is of the form $\Phi (T)=TA+BT$ for some $A,B$ in $B(X)$.


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Additional Information

Jun Zhu
Affiliation: Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei, 445000, People’s Republic of China

Changping Xiong
Affiliation: Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei, 445000, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03722-2
PII: S 0002-9939(97)03722-2
Keywords: Jordan derivation, standard operator algebra, bilocal derivation, local derivation
Received by editor(s): June 14, 1995
Received by editor(s) in revised form: November 8, 1995
Additional Notes: Project supported by the Science Foundation of HBEC, People’s Republic of China
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society