Approximative Atomic Systems for operators in Banach spaces

2019/09/11 by Shah Jahan, Jahan, Shah
Computer Science · Mathematics · #42C05 #42C15 #42C30 #46B15 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1909.05334

openalex publication_date 2019/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

K-frames and atomic systems for an operator K in Hilbert spaces were introduced by Gavruta \cite12 and further studied by Xio, Zhu and Gavruta \cite21. In this paper, we have introduced the notion of an approximative atomic system for an operator K in Banach spaces and obtained interesting results. A complete characterization of family of approximative local atoms of subspace of Banach space has been obtained. Also, a necessary and sufficient condition for the existence of an approximative atomic system for an operator K is given. Finally, explicit methods are given for the construction of an approximative atomic systems for an operator K from a given Bessel sequence and approximative X_d-Bessel sequence.

Citations

• Orthonormal bases of compactly supported wavelets

Related

• Approximative K-Atomic Decompositions and frames in Banach Spaces
• Continuous frames for unbounded operators
• Continuous generalized atomic subspaces for operators in Hilbert spaces
• Atomic decompositions for operators in reproducing kernel Hilbert spaces
• Expansion of approximate Bessel sequences to approximate Schauder frames for Banach spaces