Abstract of a paper by Peter G. Casazza, Gitta Kutyniok, Darrin Speegle and Janet C. Tremain
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.
participants (1)
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Dale Alspach