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Herz-Schur multipliers of dynamical systems

Presented by: 
Ivan Todorov Queen's University Belfast
Thursday 23rd February 2017 - 14:00 to 15:00
INI Seminar Room 2
Herz-Schur multipliers of a locally compact group, introduced by Haagerup and de Canniere in 1985, have been instrumental in operator algebra theory in a variety of contexts, in particular in the study of approximation properties of group operator algebras. They can be viewed as the invariant part of the Schur multipliers - a class of maps on B(H) with another long list of applications, e.g. in perturbation theory of linear operators. In this talk, which is based on a joint work with A. McKee and L. Turowska, I will introduce operator-valued Schur and Herz-Schur multipliers of arbitrary locally compact groups. The latter give rise to natural maps on C*- and von Neumann algebra crossed products. I will present a characterisation of operator-valued Herz-Schur multipliers as the invariant part of the operator-valued Schur multipliers, and will discuss various special cases which highlight the generality of this class of maps and their potential usefulness in subsequent research.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons