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

 

A note on invariance of spectrum
for symmetric banach $^*$-algebras


Author: Bruce A. Barnes
Journal: Proc. Amer. Math. Soc. 126 (1998), 3545-3547
MSC (1991): Primary 46K99, 46L05
MathSciNet review: 1473655
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Abstract: Let $A$ be a symmetric Banach $^*$-algebra, let $B$ be a Banach algebra, and assume that $A\subseteq B$. A result is proved giving conditions which imply that every element of $A$ has the same spectrum in both $A$ and $B$.


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Additional Information

Bruce A. Barnes
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: barnes@darkwing.uoregon.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04620-6
PII: S 0002-9939(98)04620-6
Keywords: Symmetric Banach $^*$-algebra, invariance of spectrum, $C^*$-algebra.
Received by editor(s): April 11, 1997
Communicated by: David R. Larson
Article copyright: © Copyright 1998 American Mathematical Society