This is an announcement for the paper "A decomposition theorem for frames and the Feichtinger conjecture" by Peter G. Casazza, Gitta Kutyniok, Darrin Speegle and Janet C. Tremain.

Abstract: In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in $C^{*}$-Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open problems concerning the Feichtinger Conjecture: 1. The Feichtinger Conjecture is equivalent to the conjecture that every unit norm Bessel sequence is a finite union of frame sequences. 2. Every unit norm Bessel sequence is a finite union of sets each of which is $\omega$-independent for $\ell_2$-sequences.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46C05; 42C15; 46L05

Remarks: 10 pages

The source file(s), Decomposition_PAMS_final.tex: 35701 bytes, proc-l.cls: 2486 bytes, is(are) stored in gzipped form as 0702216.tar.gz with size 12kb. The corresponding postcript file has gzipped size 89kb.

Submitted from: gitta.kutyniok@math.uni-giessen.de

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

http://front.math.ucdavis.edu/math.FA/0702216

or

http://arXiv.org/abs/math.FA/0702216

or by email in unzipped form by transmitting an empty message with subject line

uget 0702216

or in gzipped form by using subject line

get 0702216

to: math@arXiv.org.