Infinite tensor products of c* –algebras

Abstract

The infinite tensor product A – ⨂ (Aiρi) of a family of C*-algebras Ai with respect to projections ρi ∞ 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. © 1977 Pacific Journal of Mathematics. All rights reserved.