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SUMMARY:Multiplier modules of Hilbert C*-modules revisited - Michael Frank
  (Universität Leipzig)
DTSTART:20250702T143000Z
DTEND:20250702T145000Z
UID:TALK233755@talks.cam.ac.uk
DESCRIPTION:Multiplier modules of Hilbert C*-modules are one of the possib
 le tools to investigate some problems in groupoid theory. The theory of th
 em is reconsidered to obtain more properties of these special Hilbert C*-m
 odulesand to find out facts about their potentials. Several ways of their 
 definition are indicated. The property of a Hilbert C*-module to be a mult
 iplier C*-module is shown to be an invariant with respect to the considera
 tion as a left or right Hilbert C*-module in the sense of an imprimitivity
  bimodule in strong Morita equivalence theory. The interrelation of the C*
 -algebras of ''compact'' operators\, the Banach algebras of bounded module
  operators and the Banach spaces of bounded module operators of a Hilbert 
 C*-module to its C*-dual Banach C*-module\, are characterized for pairs of
  Hilbert C*-modules and their respective multiplier modules. The structure
 s on the latter are always isometrically embedded into the respective stru
 ctures on the former. Examples are given for which continuation of these k
 inds of bounded module operators from the initial Hilbert C*-module to its
  multiplier module fails\, however existing continuations turn out to be a
 lways unique. Similarly\, bounded modular functionals from both kinds of H
 ilbert C*-modules to their respective C*-algebras of coefficients are comp
 ared\, and eventually existingcontinuations are shown to be unique.
LOCATION:External
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