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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Local derivations of reflexive algebras


Author: Jing Wu
Journal: Proc. Amer. Math. Soc. 125 (1997), 869-873
MSC (1991): Primary 47D30, 47D15, 47B47
DOI: https://doi.org/10.1090/S0002-9939-97-03720-9
MathSciNet review: 1363440
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Abstract: Let $\mathcal A$ be a reflexive algebra in Banach space $X$ such that both $O_+\not =O$ and $X_-\not =X$ in $\operatorname {Lat}\,\mathcal A$, the invariant subspace lattice of $\mathcal A$, then every derivation of $\mathcal A$ into itself is spatial. Furthermore, if $X$ is additionally reflexive, then the set of all inner derivations of $\mathcal A$ into itself is topologically algebraically reflexive.


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Additional Information

Jing Wu
Affiliation: Department of Mathematics, Qufu Normal University, Qufu, Shandong, 273165, People’s Republic of China
Address at time of publication: Department of Mathematics, Yantai Teachers’ College, Yantai, Shandong, 264025, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-97-03720-9
Keywords: Reflexive algebra, derivation, local derivation
Received by editor(s): March 21, 1995
Received by editor(s) in revised form: June 12, 1995, and October 16, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society