Herz-Schur multipliers of dynamical systems

Classification of operator algebras: complexity, rigidity, and dynamics

25 April 14:00 - 15:00

Lyudmila Turowska - Chalmers/University of Gothenburg

We extend the notion of Herz-Schur multipliers to the setting of non-commutative dynamical systems: given a C*-algebra $A$, a locally compact group $G$, and an action $\alpha$ of $G$ on $A$, we define transformations on the (reduced) crossed product $A\rtimes_{r,\alpha} G$ of $A$ by $G$, which, in the case $A = \mathbb{C}$, reduce to the classical Herz-Schur multipliers. We shall also introduce Schur $A$-multipliers which, in the case $A = \mathbb{C}$, reduce to the classical measurable Schur multipliers. We establish characterisations of Schur $A$-multipliers which generalise the classical descriptions of Schur multipliers and present a transference theorem in the new setting, identifying isometrically the Herz-Schur multipliers of the dynamical system $(A,G,\alpha)$ with the invariant part of the Schur $A$-multipliers. We shall discuss special classes of Herz-Schur multipliers, in particular, those which are associated to a locally compact abelian group $G$ and its canonical action on the $C^*$-algebra $C^*(\Gamma)$ of the dual group $\Gamma$. This is a joint work with Andrew McKee and Ivan Todorov.
Marius Dadarlat
Purdue University
Søren Eilers
University of Copenhagen
Asger Törnquist
University of Copenhagen


Søren Eilers


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