The Maximal C*-Algebra of Quotients as an Operator Bimodule

Pere Ara; Martin Mathieu; Eduard Ortega

The Maximal C*-Algebra of Quotients as an Operator Bimodule

Operator Algebras 2008-10-15 v1 Functional Analysis

Authors: Pere Ara , Martin Mathieu , Eduard Ortega

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 $A\otimes_h A$ 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.

Keywords

maximal C*-algebra of quotients operator bimodule Haagerup tensor product completely bounded bimodule homomorphisms essential closed right ideals strong Morita equivalence

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@article{arxiv.0810.2500,
  title  = {The Maximal C*-Algebra of Quotients as an Operator Bimodule},
  author = {Pere Ara and Martin Mathieu and Eduard Ortega},
  journal= {arXiv preprint arXiv:0810.2500},
  year   = {2008}
}

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8 pages; submitted

The Maximal C*-Algebra of Quotients as an Operator Bimodule

Abstract

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