Vol. 67, No. 1, 1976

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The structure of standard Cāˆ—-algebras and their representations

Wai-Mee Ching

Vol. 67 (1976), No. 1, 131ā€“153

We introduce the basic structure space Ab 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 Ab. 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
Received: 10 June 1975
Revised: 16 July 1976
Published: 1 November 1976
Wai-Mee Ching