Central and convolution Herz-Schur multipliers
Journal article, 2022

In this paper we obtain descriptions of central operator-valued Schur and Herz-Schur multipliers, akin to a classical characterisation due to Grothendieck, that reveals a close link between central (linear) multipliers and bilinear multipliers into the trace class. Restricting to dynamical systems where a locally compact group acts on itself by translation, we identify their convolution multipliers as the right completely bounded multipliers, in the sense of Junge-Neufang-Ruan, of a canonical quantum group associated with the underlying group. We provide characterisations of contractive idempotent operator-valued Schur and Herz-Schur multipliers. Exploiting the link between Herz-Schur multipliers and multipliers on transformation groupoids, we provide a combinatorial characterisation of groupoid multipliers that are contractive and idempotent.


Schur multiplier



Herz-Schur multiplier


Andrew McKee

University of Bialystok

Reyhaneh Pourshahami

Kharazmi University

Ivan G. Todorov

University of Delaware

Lyudmyla Turowska

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

New York Journal of Mathematics

1076-9803 (ISSN) 10769803 (eISSN)

Vol. 28 1-43

Subject Categories

Algebra and Logic


Mathematical Analysis

More information

Latest update

7/2/2022 1