Journal of Operator Theory

Volume 59, Issue 2, Spring 2008 pp. 237-245.

Local multiplier algebras, injective envelopes, and type I W$^*$-algebras

Authors: Martin Argerami (1) and Douglas R. Farenick (2)
Author institution: (1) Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2
(2) Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2

Summary: Characterizations of those separable $C^*$-algebras that have W$^*$-algebra injective envelopes or W$^*$-algebra local multiplier algebras are presented. The $C^*$-envelope and the injective envelope of a class of operator systems that generate certain type I von Neumann algebras are also determined.

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