Herz–Schur multipliers of dynamical systems
Artikel i vetenskaplig tidskrift, 2018

We extend the notion of a Herz–Schur multiplier to the setting of non-commutative dynamical systems: given a C*-algebra A, a locally compact group G, and an action α of G on A, we define transformations on the reduced crossed product of A by α which, in the case A=C, reduce to the classical Herz–Schur multipliers. We introduce Schur A-multipliers, establish a characterisation that generalises 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,α) with the invariant part of the Schur A-multipliers. We discuss special classes of Herz–Schur multipliers, in particular, those associated to a locally compact abelian group G and its canonical action on the C*-algebra C ⁎ (Γ) of the dual group Γ.

Crossed product

Herz–Schur multiplier

Författare

A. McKee

Queen's University Belfast

I. G. Todorov

Queen's University Belfast

Nankai University

Lyudmyla Turowska

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Advances in Mathematics

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 331 387-438

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1016/j.aim.2018.04.002