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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Locally $ B\sp{\ast} $-equivalent algebras


Author: Bruce A. Barnes
Journal: Trans. Amer. Math. Soc. 167 (1972), 435-442
MSC: Primary 46K05
MathSciNet review: 0296704
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Abstract: Let A be a Banach $ ^ \ast $-algebra. A is locally $ {B^ \ast }$-equivalent if, for every selfadjoint element $ t \in A$, the closed $ ^ \ast $-subalgebra of A generated by t is $ ^\ast$-isomorphic to a $ {B^ \ast }$-algebra. In this paper it is shown that when A is locally $ {B^\ast}$-equivalent, and in addition every selfadjoint element in A has at most countable spectrum, then A is $ ^ \ast $-isomorphic to a $ {B^ \ast }$-algebra.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0296704-1
PII: S 0002-9947(1972)0296704-1
Article copyright: © Copyright 1972 American Mathematical Society