Title

A duality principle for groups

Authors

Authors

D. Dutkay; D. G. Han;D. Larson

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

J. Funct. Anal.

Keywords

Group representations; Frame vectors; Bessel vectors; Duality principle; Von Neumann algebras; II(1) factors; WEYL-HEISENBERG FRAMES; GABOR FRAMES; II1 FACTORS; REPRESENTATIONS; Mathematics

Abstract

The duality principle for Gabor frames states that a Gabor sequence obtained by a time-frequency lattice is a frame for L(2)(R(d)) 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 II(1) 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. (C) 2009 Elsevier Inc. All rights reserved.

Journal Title

Journal of Functional Analysis

Volume

257

Issue/Number

4

Publication Date

1-1-2009

Document Type

Article

Language

English

First Page

1133

Last Page

1143

WOS Identifier

WOS:000267296600008

ISSN

0022-1236

Share

COinS