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.
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Dedicated to Professor Heinz König on his 80th birthday
The first-named and the third-named author’s research was partially supported by the DGI and the European Regional Fund, jointly, through project MTM2005-00934 and, in addition, by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. The second-named author was partially supported by a Scheme 4 grant of the London Mathematical Society. Part of this paper was written during mutual visits of the second-named author to the University of Southern Denmark, Odense and the third-named author to Queen’s University Belfast and both would like to thank the respective Mathematics Departments for their hospitality.
Received: 15 July 2008
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Ara, P., Mathieu, M. & Ortega, E. The maximal C*-algebra of quotients as an operator bimodule. Arch. Math. 92, 405–413 (2009). https://doi.org/10.1007/s00013-009-2944-5
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DOI: https://doi.org/10.1007/s00013-009-2944-5