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

 

Continuity of Lie mappings of the skew elements
of Banach algebras with involution


Authors: M. I. Berenguer and A. R. Villena
Journal: Proc. Amer. Math. Soc. 126 (1998), 2717-2720
MSC (1991): Primary 46H40, 17B40
MathSciNet review: 1469400
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04569-9
PII: S 0002-9939(98)04569-9
Received by editor(s): February 7, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society