Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A note on invariance of spectrum for symmetric banach -algebras

Author(s): 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 be a symmetric Banach -algebra, let be a Banach algebra, and assume that $A\subseteq B$ . A result is proved giving conditions which imply that every element of has the same spectrum in both and .

References:

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 -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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