Quasi-multipliers of Hilbert and Banach C*-bimodules

Pavlov, Alexander, Pennig, Ulrich ORCID: https://orcid.org/0000-0001-5441-6130 and Schick, Thomas 2011. Quasi-multipliers of Hilbert and Banach C*-bimodules. Mathematica Scandinavica 109 (1) , pp. 71-92.

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Abstract

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:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Mathematica Scandinavica
ISSN:	1903-1807
Last Modified:	01 Nov 2022 09:53
URI:	https://orca.cardiff.ac.uk/id/eprint/89578

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