Title

A Duality Principle For Groups

Keywords

Bessel vectors; Duality principle; Frame vectors; Group representations; II factors 1; Von Neumann algebras

Abstract

The duality principle for Gabor frames states that a Gabor sequence obtained by a time-frequency lattice is a frame for L2 (Rd) if and only if the associated adjoint Gabor sequence is a Riesz sequence. We prove that this duality principle extends to any dual pairs of projective unitary representations of countable groups. We examine the existence problem of dual pairs and establish some connection with classification problems for II1 factors. While in general such a pair may not exist for some groups, we show that such a dual pair always exists for every subrepresentation of the left regular unitary representation when G is an abelian infinite countable group or an amenable ICC group. For free groups with finitely many generators, the existence problem of such a dual pair is equivalent to the well-known problem about the classification of free group von Neumann algebras. © 2009 Elsevier Inc. All rights reserved.

Publication Date

8-15-2009

Publication Title

Journal of Functional Analysis

Volume

257

Issue

4

Number of Pages

1133-1143

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jfa.2009.03.007

Socpus ID

67349257811 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/67349257811

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