Commutative non-Archimedean C^∗-algebras

Gerard J. Murphy

Vol. 78 (1978), No. 2, 433–446

DOI: 10.2140/pjm.1978.78.433

Abstract

Commutative non-archimedean C^∗-algebras are defined, their properties established, and a representation theory is developed for them. Their closed ideals are completely analyzed in terms of the closed subsets of the spectrum where they ‘vanish.’ A large class of C^∗-algebras is exhibited. A Stone-Weierstrass theorem generalizing a result of Kaplansky is proved.

Mathematical Subject Classification 2000

Primary: 46P05, 46P05

Secondary: 46J99

Milestones

Received: 28 May 1976

Revised: 20 May 1977

Published: 1 October 1978