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Proceedings of the American Mathematical Society

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

 

 

Affine mappings of invertible operators


Authors: Lawrence A. Harris and Richard V. Kadison
Journal: Proc. Amer. Math. Soc. 124 (1996), 2415-2422
MSC (1991): Primary 46L05
MathSciNet review: 1340389
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Abstract: The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.


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Additional Information

Lawrence A. Harris
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027

Richard V. Kadison
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395

DOI: https://doi.org/10.1090/S0002-9939-96-03445-4
Keywords: Banach algebra, C*-algebra, invertible elements
Received by editor(s): February 13, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society