Vol. 72, No. 2, 1977

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Infinite tensor products of Cāˆ—-algebras

Bruce Blackadar

Vol. 72 (1977), No. 2, 313ā€“334

The infinite tensor product A = (Ai,pi) of a family of C-algebras Ai with respect to projections pi Ai is examined. The primitive ideal space and the characters of A are completely described in the case where each Ai is simple, or separable and nuclear. If A is not type I, an explicit construction is given of a factor representation of A generating an arbitrary hyperfinite factor. In addition, new results are obtained about primitive ideals and characters of a tensor product of two C-algebras. Examples are given of various phenomena, providing solutions to previously published problems.

Mathematical Subject Classification 2000
Primary: 46L05
Secondary: 46M05
Received: 17 February 1976
Published: 1 October 1977
Bruce Blackadar