The structure of standard<i>C</i>^∗-algebras and their representations

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 PP^-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*-aigebras 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. ! Introduction* The Wedderburn structure theorem asserts 1