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Proceedings of the American Mathematical Society

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Commutativity criteria for Banach $^*$-algebras


Authors: L. C. Leinbach and Bertram Yood
Journal: Proc. Amer. Math. Soc. 125 (1997), 2307-2312
MSC (1991): Primary 46H10
MathSciNet review: 1389526
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Abstract: Let $A$ be a Banach $^*$-algebra with an identity. Necessary and sufficient conditions are given for $A$ to be commutative modulo its $^*$-radical and for $A$ to be commutative if $A$ has a faithful $^*$-representation as operators on a Hilbert space.


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Additional Information

L. C. Leinbach
Affiliation: Department of Mathematics, Gettysburg College, Gettysburg, Pennsylvania 17325

Bertram Yood
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03854-9
Received by editor(s): October 12, 1995
Received by editor(s) in revised form: January 30, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society