The structure of standard C^∗-algebras and their representations

Wai-Mee Ching

Vol. 67 (1976), No. 1, 131–153

DOI: 10.2140/pjm.1976.67.131

Abstract

We introduce the basic structure space A^b of a C^∗-algebra A consisting of all minimal primitive ideals in A. We define a class of C^∗-algebras to be called standard. All W^∗-algebras and all C^∗-algebras with Hausdorff structure spaces are standard. It is proved that a standard C^∗-algebra A is isometrically isomorphic to the C^∗-algebrade fined by a continuous field of primitive C^∗-algebras over its basic structure space A^b. A sufficient condition for a C^∗-algebra to be faithfully represented on a separable Hibert space is also presented.

Mathematical Subject Classification 2000

Primary: 46L05

Milestones

Received: 10 June 1975

Revised: 16 July 1976

Published: 1 November 1976