Quasi-multipliers of Hilbert and Banach C*-bimodules

• Autores: Alexander Pavlov, Ulrich Pennig, Thomas Schick
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 109, Nº 1, 2011, págs. 71-92
• Idioma: inglés
• DOI: 10.7146/math.scand.a-15178
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• Resumen

  • Quasi-multipliers for a Hilbert C∗-bimodule V were introduced by L. G. Brown, J. A. Mingo, and N.-T. Shen [3] 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 l2(A) and for bimodules of sections of Hilbert C∗-bimodule bundles over locally compact spaces.