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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Representation of $ A$-convex algebras


Author: Allan C. Cochran
Journal: Proc. Amer. Math. Soc. 41 (1973), 473-479
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9939-1973-0333735-3
MathSciNet review: 0333735
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Abstract: Algebraic properties of $ A$-convex algebras are developed via a functor to locally $ m$-convex algebras. The Gel'fand-Mazur theorem holds for $ A$-convex algebras, and this fact allows a Gel'fand-type representation theorem for a subclass of uniformly $ A$-convex algebras. Connections to existing functional representation theory are also obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0333735-3
Keywords: $ A$-convex algebra, locally $ m$-convex algebra, Gel'fand-Mazur theorem, strict topology, compact-open topology, Gel'fand representation theorem
Article copyright: © Copyright 1973 American Mathematical Society