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Department Colloquium

Fri., Jan. 29, 2021 3:30 p.m.

Location: Live Stream

Speaker: Jason Crann, Carleton University

Title:  Amenable dynamical systems through Herz-Schur multipliers (511 kB) PDF file


The Herz-Schur multiplier manifestation of amenability provides a fundamental link between abstract harmonic analysis and operator algebras, allowing for a fruitful exchange of ideas and tools between the two areas. A generalized theory of Herz--Schur multipliers for dynamical systems has recently emerged through independent work of Bedos-Conti and McKee-Todorov-Turowska.

In this talk, we generalize the aforementioned link by establishing Herz--Schur multiplier characterizations of amenable W*- and C*-dynamical systems over arbitrary locally compact groups. As byproducts of our results, we (1) answer a question of Anantharaman-Delaroche and obtain a Reiter type characterization of amenable W*-dynamical systems, and (2) show that a commutative C*-dynamical system (C_0(X),G,alpha) is amenable if and only if the action of G on X is topologically amenable. Combined with recent work of Buss-Echterhoff-Willett, this latter result implies the equivalence between topological amenability and measurewise amenabilty for G-spaces X when both G and X are second countable. This is joint work with Alex Bearden.

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