2009/11/30 by Wayne Lawton, W. Lawton, Lawton, W. · 2 citations
Mathematics · #37B10 #42A55 #46L05 #Advanced Operator Algebra Research #Bounded function #Combinatorics #Conjecture #Diagonal #Discrete mathematics #Dynamical Systems (math.DS) #Exponential function #Extension (predicate logic) #FOS: Mathematics #Function (biology) #Functional Analysis (math.FA) #Hilbert space #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Pure mathematics #Separable space #Sequence (biology) #Spectral Theory in Mathematical Physics #Subsequence #math.DS #math.FA #msc:37B10 #msc:42A55 #msc:46L05
paper · pdf · doi:10.48550/arxiv.0911.5559
published in UWA Profiles and Research Repository (University of Western Australia) (The University of Western Australia) · 10 pages, Theorem 1.1 was announced during conferences in St. Petersburg, Russia, June 14-20, 2009, and in Kuala Lumpur, Malaysia, June 22-26, 2009
arxiv created 2009/11/30 · openalex publication_date 2009/11/30 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Kadison-Singer problem asks: does every pure state on the diagonal sublgebra of the C*-algebra of bounded operators on a separable infinite dimensional Hilbert space admit a unique extension? A yes answer is equivalent to several open conjectures including Feichtinger's: every bounded frame is a finite union of Riesz sequences. We consider the special case: Feichtinger's conjecture for exponentials and prove that the set of projections onto a measurable subset of the circle group of the set of exponential functions equals a union of a finite number of Reisz sequences if and only if there exists a Reisz subsequence corresponding to integers whose characteristic function is a nonzero minimal sequence.