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
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