On the sum of generalized frames in Hilbert spaces
type: Item
instance of: scholarly article
title: On the sum of generalized frames in Hilbert spaces
zbMATH Open document ID: 1478.42030
author: Fatemeh Abtahi
author: Zeinab Kamali
author: Zahra Keyshams
published in: Mediterranean Journal of Mathematics
publication date: 2021-08-30T00:00:00Z
review text: The paper deals with \(K\)-frames, \(K\)-\(g\)-frames and controlled frames in Hilbert spaces. The main results are the following. \par i) Let \(\{f_n\}\) be a Bessel sequence of a Hilbert space \(\mathcal{H}\) and \(\mathcal{KF}\) the set of operators \(K\in \mathcal{B}(\mathcal{H})\) such that \(\{f_n\}\) is a \(K\)-frame. Then \(\mathcal{KF}\) is a right ideal (but not necessarily a left ideal) of \(\mathcal{B}(\mathcal{H})\). \par ii) Sufficient conditions for the finite sum of \(K\)-frames to be a \(K\)-frame. \par iii) Results of the same type about \(K\)-\(g\)-frames and controlled frames. The paper contains also some examples related to the results.
reviewed by: Rosario Corso
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 46C07
zbMATH DE Number: 7388018
zbMATH Keywords: controlled frame
zbMATH Keywords: frame
zbMATH Keywords: \(K\)-frame
zbMATH Keywords: \(K\)-\(g\)-frame
zbMATH Keywords: synthesis operator
MaRDI profile type: Publication
full work available at URL: s00009-021-01811-8
OpenAlex ID: W3179216521
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DOI: 10.1007/S00009-021-01811-8
description: scientific article; zbMATH DE number 7388018