Herz-Schur multipliers of dynamical systems

A. McKee, I. G. Todorov, L. Turowska

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
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Abstract

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 , 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 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 of the dual group Γ.
Original languageEnglish
Pages (from-to)387-438
Number of pages52
JournalAdvances in Mathematics
Volume331
Early online date20 Jun 2018
DOIs
Publication statusPublished - 20 Jun 2018

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