Vol. 44, No. 1, 1973

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Function algebras over valued fields

George Bachman, Edward Beckenstein and Lawrence Narici

Vol. 44 (1973), No. 1, 45–58
Abstract

In this paper we consider primarily algebras F(T) of continuous funtions taking a topological space T into a complete nonarchimedean nontrivially valued field F. Some general properties of function algebras and topological algebras over valued fields are developed in §§1 and 2. Some principal results (Theorems 6 and 7) are analogs of theorems of Nachbin and Shirota, and Warner: Essentially that F(T) with compact-open topology is F-barreled iff unbounded functions exist on closed noncompact subsets of T; and that full Fréchet algebras are realizable as function algebras F(,) where denotes the space of nontrivial continuous homomorphisms of the algebra.

Mathematical Subject Classification 2000
Primary: 46J99
Milestones
Received: 7 June 1971
Published: 1 January 1973
Authors
George Bachman
Edward Beckenstein
Lawrence Narici