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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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Continuity of Lie mappings of the skew elements of Banach algebras with involution
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by M. I. Berenguer and A. R. Villena PDF
Proc. Amer. Math. Soc. 126 (1998), 2717-2720 Request permission

Abstract:

Let $A$ and $B$ be centrally closed prime complex Banach algebras with linear involution. If $A$ is semisimple, then any Lie derivation of the skew elements of $A$ is continuous and any Lie isomorphism from the skew elements of $B$ onto the skew elements of $A$ is continuous.
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Additional Information
  • M. I. Berenguer
  • Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
  • A. R. Villena
  • Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
  • Email: avillena@goliat.ugr.es
  • Received by editor(s): February 7, 1997
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2717-2720
  • MSC (1991): Primary 46H40, 17B40
  • DOI: https://doi.org/10.1090/S0002-9939-98-04569-9
  • MathSciNet review: 1469400