Syndetic sets, paving and the Feichtinger conjecture

Author:
Vern I. Paulsen

Journal:
Proc. Amer. Math. Soc. **139** (2011), 1115-1120

MSC (2000):
Primary 46L05; Secondary 46B15

DOI:
https://doi.org/10.1090/S0002-9939-2010-10600-7

Published electronically:
August 12, 2010

MathSciNet review:
2745663

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if a Bessel sequence in a Hilbert space that is indexed by a countably infinite group in an invariant manner can be partitioned into finitely many Riesz basic sequences, then each of the sets in the partition can be chosen to be syndetic. We then apply this result to prove that if a Fourier frame for a measurable subset of a higher dimensional cube can be partitioned into Riesz basic sequences, then each subset can be chosen to be a syndetic subset of the corresponding higher dimensional integer lattice. Both of these results follow from a result about syndetic pavings of elements of the von Neumann algebra of a discrete group.

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Additional Information

**Vern I. Paulsen**

Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476

Email:
vern@math.uh.edu

DOI:
https://doi.org/10.1090/S0002-9939-2010-10600-7

Received by editor(s):
April 12, 2010

Published electronically:
August 12, 2010

Additional Notes:
This research was supported in part by NSF grant DMS-0600191 and by the American Institute of Mathematics.

Communicated by:
Michael T. Lacey

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.