Representation of 𝐴-convex algebras

Cochran, Allan C.

doi:10.1090/S0002-9939-1973-0333735-3

Representation of $A$-convex algebras
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Proc. Amer. Math. Soc. 41 (1973), 473-479 Request permission

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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