This is an announcement for the paper "Spanning and independence properties of frame partitions" by Bernhard G. Bodmann, Peter G. Casazza, Vern I. Paulsen, and Darrin Speegle.

Abstract: We answer a number of open problems in frame theory concerning the decomposition of frames into linearly independent and/or spanning sets. We prove that in finite dimensional Hilbert spaces, Parseval frames with norms bounded away from 1 can be decomposed into a number of sets whose complements are spanning, where the number of these sets only depends on the norm bound. We also prove, assuming the Kadison-Singer conjecture is true, that this holds for infinite dimensional Hilbert spaces. Further, we prove a stronger result for Parseval frames whose norms are uniformly small, which shows that in addition to the spanning property, the sets can be chosen to be independent, and the complement of each set to contain a number of disjoint, spanning sets.

Archive classification: math.FA math.OA

Submitted from: vern@math.uh.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1004.2446

or

http://arXiv.org/abs/1004.2446