Analysis Seminar: Lyudmila Turowska (Chalmers University of Technology, Sweden)

Sets of multiplicity and closable multipliers on group algebras

    W. Arveson in his fundamental paper (Ann. Math., 1974) discovered an interplay be-
tween the invariant subspace and operator algebra theory and spectral synthesis in
harmonic analysis. We develop further his ideas and establish new connections with
harmonic analysis, in particular, sets of multiplicity (M-sets). M-sets in commutative
harmonic analysis arose in connection with problems of uniqueness of triginometric
series. J. Froelich (J. Funct. Anal., 1988) found a connection between M -sets and the
property of operator algebra associated with a commutative subspace lattice to con-
tain a nonzero compact operator. Recently we observed also a connection with the
property of certain Schur type transformations on the space of compact operators to
be closable. This motivated us to generalise the notion of multiplicity sets to general lo-
cally compact groups, define their operator counterparts and study multipliers of group
algebras closable in different topologies. In this talk we will discuss the notions, their
properties and connection with operator theory. This is a joint work with V. Shulman
and I. Todorov.

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Her visit is supported by an LMS Scheme 2 grant.

Location: TR3(?), Herschel Building
Date/Time: 4th October 2012, 16:00 - 17:00

Published: 6th July 2012