Non-Archimedean Gel’fand theory

Jesus M. Dominguez

Vol. 104 (1983), No. 2, 337–341

DOI: 10.2140/pjm.1983.104.337

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