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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 | References | Similar Articles | Additional Information

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 $B$.

References [Enhancements On Off] (What's this?)

  • 1. F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, Berlin, 1973. MR 54:11013
  • 2. S. Cleveland, Homomorphisms of non-commutative $^*$-algebras, Pacific J. Math. 13 (1963), 1097-1109. MR 28:1500
  • 3. J. Daughtry, A. Lambert, and B. Weinstock, Invariance of spectrum for representations of $C^*$-algebras on Banach spaces, Proceedings of the AMS 125 (1997), 189-198. MR 97c:46067
  • 4. C. Rickart, Banach Algebras, Van Nostrand, 1960.

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Additional Information

Bruce A. Barnes
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403

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

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