Multiplier modules of Hilbert C*-modules revisited

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• Michael Frank (Universität Leipzig)
• Wednesday 02 July 2025, 15:30-15:50
• External.

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TGAW01 - Crossed products and groupoid C*-algebras

Multiplier modules of Hilbert C-modules are one of the possible tools to investigate some problems in groupoid theory. The theory of them is reconsidered to obtain more properties of these special Hilbert C-modulesand to find out facts about their potentials. Several ways of their definition are indicated. The property of a Hilbert C-module to be a multiplier C-module is shown to be an invariant with respect to the consideration 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 structures on the latter are always isometrically embedded into the respective structures on the former. Examples are given for which continuation of these kinds of bounded module operators from the initial Hilbert C-module to its multiplier module fails, however existing continuations turn out to be always unique. Similarly, bounded modular functionals from both kinds of Hilbert C-modules to their respective C*-algebras of coefficients are compared, and eventually existingcontinuations are shown to be unique.

This talk is part of the Isaac Newton Institute Seminar Series series.

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