Title

Parseval Frames For Icc Groups

Keywords

II -factors 1; Kadison-Singer problem; Parseval frames; Undersampling

Abstract

We analyze Parseval frames generated by the action of an ICC group on a Hilbert space. We parametrize the set of all such Parseval frames by operators in the commutant of the corresponding representation. We characterize when two such frames are strongly disjoint. We prove an undersampling result showing that if the representation has a Parseval frame of equal norm vectors of norm frac(1, sqrt(N)), the Hilbert space is spanned by an orthonormal basis generated by a subgroup. As applications we obtain some sufficient conditions under which a unitary representation admits a Parseval frame which is spanned by a Riesz sequences generated by a subgroup. In particular, every subrepresentation of the left-regular representation of a free group has this property.

Publication Date

5-1-2009

Publication Title

Journal of Functional Analysis

Volume

256

Issue

9

Number of Pages

3071-3090

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jfa.2008.11.017

Socpus ID

62049084509 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/62049084509

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