A Decomposition Theorem for frames and the Feichtinger Conjecture

dc.creatorCasazza, Peter G.
dc.creatorKutyniok, Gitta
dc.creatorSpeegle, Darrin
dc.creatorTremain, Janet C.
dc.date2007-02-08
dc.date.accessioned2026-07-07T07:45:36Z
dc.date.available2026-07-07T07:45:36Z
dc.descriptionIn 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 $ω$-independent for $\ell_2$-sequences.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0702216
dc.identifierhttp://arxiv.org/abs/math/0702216
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123581
dc.subjectFunctional Analysis
dc.subject46C05; 42C15; 46L05
dc.titleA Decomposition Theorem for frames and the Feichtinger Conjecture
dc.typetext

Files

Collections