Atomic systems for operators-Reference-Cited by-同舟云学术

Atomic systems for operators

Published:2019-01 Issue:01 Volume:17 Page:1850066
ISSN:0219-6913
Container-title:International Journal of Wavelets, Multiresolution and Information Processing
language:en
Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.

Author:

Poumai Khole Timothy¹,Jahan Shah²

Affiliation:

1. Department of Mathematics, Motilal Nehru College, University of Delhi, Delhi-110021, India

2. Department of Mathematics, University of Delhi, Delhi-110007, India

Abstract

Gavruta [L. Gavruta, Frames for operators, Appl. Comput. Harmon. Anal. 32 (2012) 139–144] introduced the notion of [Formula: see text]-frame and atomic system for an operator [Formula: see text] in Hilbert spaces. We extend these notions to Banach spaces and obtain various new results. A necessary and sufficient condition for the existence of an atomic system for an operator [Formula: see text] in a Banach space is given. Also, a characterization for the family of local atoms of subspaces of Banach spaces has been given. Further, we give methods to construct an atomic system for an operator [Formula: see text] from a given Bessel sequence and an [Formula: see text]-Bessel sequence. Finally, a result related to stability of atomic system for an operator [Formula: see text] in a Banach space has been given.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Information Systems,Signal Processing

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219691318500662

Reference22 articles.

1. Majorization, range inclusion, and factorization for bounded linear operators

2. Perturbation of operators and applications to frame theory

3. Frame expansions in separable Banach spaces

4. An Introduction to Frames and Riesz Bases

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Duality of Continuous K-g-Frames;SAHAND COMMUN MATH A;2023

2. On K-woven frames in Hilbert $$C^{*}$$-modules;Journal of Pseudo-Differential Operators and Applications;2022-08-20

3. On K-duality and redundancy of K-g-frames;Ricerche di Matematica;2021-06-07

4. On K-frame generators for unitary systems in Hilbert $$C^{*}$$-modules;Journal of Pseudo-Differential Operators and Applications;2021-02-12

5. Some New Results of Weaving K-Frames in Hilbert Spaces;Numerical Functional Analysis and Optimization;2021-02-11