Feichtinger Conjectures, R_ε-Conjectures and Weaver's Conjectures for Banach spaces

2022/01/01 by K. Mahesh Krishna, Krishna, K. Mahesh
Computer Science · #11K38 #14Q15 #42C15 #46B04 #46B45 #46L05 #94A20 #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Optical measurement and interference techniques

paper · pdf · doi:10.48550/arxiv.2201.00125

openalex publication_date 2022/01/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Motivated from two decades old famous Feichtinger conjectures for frames, R_ε-conjecture and Weaver's conjecture for Hilbert spaces (and their solution by Marcus, Spielman, and Srivastava), we formulate Feichtinger conjectures for p-approximate Schauder frames, R_ε-conjecture, Weaver's conjectures and Akemann-Weaver conjectures for Banach spaces. We also formulate conjectures on p-approximate Schauder frames based on the results of Casazza for frames for Hilbert spaces. We state conjectures and problems for p-approximate Schauder frames based on fundamental inequality for frames for Hilbert spaces and scaling problem for Hilbert space frames. Based on Kothe-Lorch theorem for Riesz bases for Hilbert spaces, we formulate a problem for p-approximate Riesz bases for Banach spaces. We formulate dynamical sampling problem for p-approximate Schauder frames for Banach spaces. We ask phase retrieval problem and norm retrieval problem for p-approximate Schauder frames for Banach spaces. We also formulate discretization problem for continuous p-approximate Schauder frames.

Related

• Weaving Schauder frames
• The (abc,pqr)-problem for Approximate Schauder Frames for Banach Spaces
• Localized Bounded Below Approximate Schauder Frames are Finite Unions of Approximate Riesz Sequences
• Perturbation of p-approximate Schauder frames for separable Banach spaces
• Operator-Valued p-Approximate Schauder Frames