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

2008/10/14 by Ara, Pere, Mathieu, Martin, Ortega, Eduard
#16 D90 #46A13 #46H25 #46L05 #46L07 #47L25 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.0810.2500

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⊗_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.

Related

• Bimodule maps from a unital C^*-algebra to its C^*-subalgebra and strong Morita equivalence
• On Morita's Fundamental Theorem for C*-algebras
• Tensor products of maximal abelian subalgebras of C*-algebras
• On maximal tensor products and quotient maps of operator systems
• Countable Degree-1 Saturation of Certain C*-Algebras Which Are Coronas\n of Banach Algebras