The Maximal C*-Algebra of Quotients as an Operator Bimodule
Abstract
We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product Ah A labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved.
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