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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Local derivations of reflexive algebras
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by Jing Wu PDF
Proc. Amer. Math. Soc. 125 (1997), 869-873 Request permission

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.
References
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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
  • 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
  • © Copyright 1997 American Mathematical Society
  • 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