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

 

Function representation of a noncommutative uniform algebra


Author: Krzysztof Jarosz
Journal: Proc. Amer. Math. Soc. 136 (2008), 605-611
MSC (2000): Primary 46H20, 46H05
Published electronically: November 1, 2007
MathSciNet review: 2358502
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Abstract: We construct a Gelfand type representation of a real noncommutative Banach algebra $ A$ satisfying $ \left\Vert f^{2}\right\Vert =\left\Vert f\right\Vert ^{2}$, for all $ f\in A.$


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Additional Information

Krzysztof Jarosz
Affiliation: Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, Illinois 62026-1653
Email: kjarosz@siue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09033-8
PII: S 0002-9939(07)09033-8
Keywords: Uniform algebra, function algebra, Banach algebra, quaternions
Received by editor(s): October 31, 2005
Received by editor(s) in revised form: November 24, 2006
Published electronically: November 1, 2007
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.