Completely Compact Herz-Schur Multipliers of Dynamical Systems
Journal article, 2022

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 (sic)(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 (sic)(r,alpha) G and provide a description of this class in the case of the irrational rotation algebra.

Multiplier

Completely compact map

Crossed product

Author

Weijiao He

Taiyuan Normal University

Ivan G. Todorov

University of Delaware

Lyudmyla Turowska

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

Journal of Fourier Analysis and Applications

1069-5869 (ISSN) 15315851 (eISSN)

Vol. 28 3 47

Subject Categories

Mathematical Analysis

DOI

10.1007/s00041-022-09942-6

More information

Latest update

7/2/2022 1