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arXiv · 2107.03386

Completely compact Herz-Schur multipliers of dynamical systems

Weijiao He·Ivan G. Todorov·L. Turowska
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Abstract

We prove that if $G$ is a discrete group and $(A,G,\alpha)$ is a C*-dynamical system such that the reduced crossed product $A\rtimes_{r,\alpha} G$ possesses property (SOAP) then every completely compact Herz-Schur $(A,G,\alpha)$-multiplier can be approximated in the completely bounded norm by Herz-Schur $(A,G,\alpha)$-multipliers of finite rank. As a consequence, if $G$ has the approximation property (AP) then the completely compact Herz-Schur multipliers of $A(G)$ coincide with the closure of $A(G)$ in the completely bounded multiplier norm. We study the class of invariant completely compact Herz-Schur multipliers of $A\rtimes_{r,\alpha} G$ and provide a description of this class in the case of the irrational rotation algebra.

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Weijiao He, Ivan G. Todorov, L. Turowska. 2021-07-07. Completely compact Herz-Schur multipliers of dynamical systems. https://arxiv.org/abs/2107.03386

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