A note on operator perturbation of woven frames
type: Item
instance of: scholarly article
title: A note on operator perturbation of woven frames
zbMATH Open document ID: 1483.42021
author: Zhongqi Xiang
author: Xiangchun Xiao
published in: Proceedings of the Japan Academy. Series A
publication date: 2022-02-14T00:00:00Z
review text: The paper deals with the operator perturbation of woven frames. The motivation is due to known result [\textit{A. Rahimi} et al., Int. J. Wavelets Multiresolut. Inf. Process. 17, No. 3, Article ID 1950010, 15 p. (2019; Zbl 1417.42037)] which stated that bounded linear operators preserve woven frames if and only if they are invertible. Although, a counter example shows that the ``only if'' part of the result is not true. A correction to this result with some other new results on the stability of woven frames under operator perturbation of two different operators have been given.
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 7473075
zbMATH Keywords: operator perturbation
zbMATH Keywords: pseudo-inverse
zbMATH Keywords: weaving frame
zbMATH Keywords: woven frame operator
reviewed by: Devendra Kumar
MaRDI profile type: Publication
full work available at URL: pjaa.97.017
OpenAlex ID: W4200557548
cites work: Weaving frames
cites work: Characterizations of weaving \(K\)-frames
cites work: Characterizations of woven frames
cites work: An introduction to frames and Riesz bases
cites work: Characterizations of function spaces on the sphere using frames
cites work: Painless nonorthogonal expansions
cites work: Q4623056
cites work: Weaving \(K\)-frames in Hilbert spaces
cites work: A Class of Nonharmonic Fourier Series
cites work: Q4365116
cites work: Weaving \(g\)-frames and weaving fusion frames
cites work: On weaving g-frames for Hilbert spaces
cites work: Paley-Wiener-Schwartz nearly Parseval frames on noncompact symmetric spaces
cites work: A consistent and stable approach to generalized sampling
cites work: Frame-related operators for woven frames
DOI: 10.3792/PJAA.97.017
description: scientific article; zbMATH DE number 7473075