Journal of Operator Theory

Volume 39, Issue 1, Winter 1998 pp. 113-121.

The central Haagerup tensor product of a

$C^*$ -algebra

Authors: D.W.B. Somerset
Author institution: Department of Mathematical Sciences, University of Aberdeen, AB24 3UE, U.K.

Summary: Let

$A$ be a

$C^*$ -algebra with an identity and let

$\theta_Z$ be the canonical map from

$A\otimes_Z A$ , the central Haagerup tensor product of

$A$ , to

$CB(A)$ , the algebra of completely bounded operators on

$A$ . It is shown that if every Glimm ideal of

$A$ is primal then

$\theta_Z$ is an isometry. This covers unital quasi-standard

$C^*$ -algebras and quotients of AW

$^*$ -algebras.

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