Approximate identities and the strict topology

Heron S. Collins and Robert A. Fontenot

Vol. 43 (1972), No. 1, 63–79

DOI: 10.2140/pjm.1972.43.63

Abstract

This paper studies relationships between approximate identities on a B^∗ algebra A and other properties of the algebra. If A is commutative, conditions on the approximate identity for A are related to topological properties of the spectrum of A. The principal result of this paper is that for a locally compacl Hausdorff space S,C₀(S) has an approximate identity that is totally bounded in the strict topology (or compact open topology) if and only if S is paracompact.

Mathematical Subject Classification 2000

Primary: 46K05

Milestones

Received: 1 June 1971

Published: 1 October 1972