Vol. 104, No. 2, 1983

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Non-Archimedean Gel’fand theory

Jesus M. Dominguez

Vol. 104 (1983), No. 2, 337–341
Abstract

In this paper we show that if X is a Banach algebra and X0 is its Gelfand subalgebra, then the set X0 of the elements in X0 with compact spectrum is a Gelfand algebra whose maximal ideal space is compact in the Gelfand topology. We also give a representation theorem for X0, which we use to derive the Van der Put characterization of C-algebras.

Mathematical Subject Classification 2000
Primary: 46P05, 46P05
Secondary: 46J20
Milestones
Received: 25 February 1981
Revised: 5 October 1981
Published: 1 February 1983
Authors
Jesus M. Dominguez