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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Derivations mapping into the socle, II
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by Matej Brešar
Proc. Amer. Math. Soc. 126 (1998), 181-187
DOI: https://doi.org/10.1090/S0002-9939-98-03993-8

Abstract:

Let $\mathcal A$ be a unital Banach algebra. Several characterizations of continuous derivations of $\mathcal A$ having only elements with finite spectrum in their ranges are obtained. In particular, if $\mathcal A$ is semisimple, then such derivations map $\mathcal A$ into its socle.
References
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Bibliographic Information
  • Matej Brešar
  • Affiliation: Department of Mathematics, University of Maribor, PF, Koroška 160, 62000 Maribor, Slovenia
  • Email: bresar@uni-mb.sl
  • Received by editor(s): March 20, 1996
  • Received by editor(s) in revised form: July 8, 1996
  • Additional Notes: The author was supported in part by a grant from the Ministry of Science of Slovenia
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 181-187
  • MSC (1991): Primary 46H05
  • DOI: https://doi.org/10.1090/S0002-9939-98-03993-8
  • MathSciNet review: 1416078