G-frame operator distance problems
type: Item
instance of: scholarly article
title: G-frame operator distance problems
zbMATH Open document ID: 1467.42047
author: Miao He
author: Yuxiang Xu
author: Jinsong Leng
published in: Annals of Functional Analysis
publication date: 2021-06-18T00:00:00Z
review text: This paper discusses the g-frame operator distance problems. G-frame serves as a special type of frame, which combines operator theory with frame theory. In fact, since the frame elements of g-frames are operators, the frame operator of a g-frame has a different form. The paper gives a new method to describe the distance of two g-frames. The authors find some properties of frame operator distance problems still hold in the \(\mathrm{g}\)-frame operator distance problems. The existence of a local minimizer of \(\Theta(G)=L\left(A-S_{G}\right)\) is studied and some properties of \(G=\left\{\Lambda_{i}\right\}_{i=1}^{n}\) are discussed, when \(G=\left\{\Lambda_{i}\right\}_{i=1}^{n}\) is a local minimizer of \(\Theta(L, A, a)\). Moreover, some special situations such that a local minimizer is a global minimizer are explored.
reviewed by: Pierluigi Vellucci
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 46C07
zbMATH DE Number: 7360833
zbMATH Keywords: matrix approximation
zbMATH Keywords: majorization
zbMATH Keywords: g-frames operator
MaRDI profile type: Publication
full work available at URL: s43034-021-00126-9
OpenAlex ID: W3160556515
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DOI: 10.1007/S43034-021-00126-9
description: scientific article; zbMATH DE number 7360833