Which multiplier algebras are W^*-algebras?

2013/04/28 by Charles A. Akemann, Akemann, Charles A., Massoud Amini +3
Mathematics · #47L30 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L10 #Secondary 46L08 #math.OA #msc:46L08 #msc:46L10 #msc:47L30

paper · pdf · doi:10.48550/arxiv.1304.7453

arxiv created 2013/04/28 · arxiv updated 2013/04/30

Abstract

We consider the question of when the multiplier algebra M(A) of a C^*-algebra A is a W^*-algebra, and show that it holds for a stable C^*-algebra exactly when it is a C^*-algebra of compact operators. This implies that if for every Hilbert C^*-module E over a C^*-algebra A, the algebra B(E) of adjointable operators on E is a W^*-algebra, then A is a C^*-algebra of compact operators. Also we show that a unital C^*-algebra A which is Morita equivalent to a W^*-algebra must be a W^*-algebra.

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