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Quasi-multipliers of Hilbert and Banach C*-bimodules

Pavlov, Alexander, Pennig, Ulrich and Schick, Thomas 2011. Quasi-multipliers of Hilbert and Banach C*-bimodules. Mathematica Scandinavica 109 (1) , pp. 71-92.

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Quasi-multipliers for a Hilbert C*-bimodule V were introduced by L. G. Brown, J. A. Mingo, and N.-T. Shen as a certain subset of the Banach bidual module V**. We give another (equivalent) definition of quasi-multipliers for Hilbert C*-bimodules using the centralizer approach and then show that quasi-multipliers are, in fact, universal (maximal) objects of a certain category. We also introduce quasi-multipliers for bimodules in Kasparov's sense and even for Banach bimodules over C*-algebras, provided these C*-algebras act non-degenerately. A topological picture of quasi-multipliers via the quasi-strict topology is given. Finally, we describe quasi-multipliers in two main situations: for the standard Hilbert bimodule and for bimodules of sections of Hilbert C*-bimodule bundles over locally compact spaces.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Mathematica Scandinavica
ISSN: 1903-1807
Last Modified: 01 May 2019 10:57

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