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Completely bounded mappings and simplicial complex structure in the primitive ideal space of a $C^*$-algebra

2008
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Transactions of the American Mathematical Society
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We consider the natural contraction from the central Haagerup tensor product of a C*-algebra A with itself to the space of completely bounded maps CB(A) on A and investigate those A where there exists an inverse map with finite norm L(A). We show that a stabilised version L (A) = sup n L(M n (A)) depends only on the primitive ideal space Prim(A). The dependence is via simplicial complex structures (defined from primal intersections) on finite sets of primitive ideals that contain a Glimm ideal

doi:10.1090/s0002-9947-08-04666-7
fatcat:5jnd4oaszzhd7nope6pz6kgeci