Tight \(K\)-\(g\)-frame and its novel characterizations via atomic systems
type: Item
instance of: scholarly article
title: Tight \(K\)-\(g\)-frame and its novel characterizations via atomic systems
zbMATH Open document ID: 1408.42024
DOI: 10.1155/2016/3783456
author: Yongdong Huang
author: Dingli Hua
published in: Advances in Mathematical Physics
publication date: 2018-10-17T00:00:00Z
review text: The authors characterize tight \(K\)-\(g\)-frames, a generalization of ordinary frames introduced by \textit{Y. Zhou} and \textit{Y. Zhu} [Acta Math. Sin., Chin. Ser. 56, No. 5, 799--806 (2013; Zbl 1299.42109)]. Although it is mentioned that this has been done via atomic systems, there is no explicit definition of atomic systems and their connection with this class of frames. The authors also study some properties of \(K\)-\(g\)-frames. In my view, some of the results are so obvious that there is no need for a proof, but the proofs are accurate and some helpful examples are included. Specific comments: (1) On page 2 Lemma 9, in condition (2) it would be better to mention that \(\{\Gamma_j\}_{j\in J}\) is the pointed \(g\)-Bessel sequence. (2) On page 6 the line number 5 from the top on the left hand, \(K^\ast f\in H\) should be changed to \(K_1^\ast f\in H\) and also all three lines 5 to 7 are not a reason for \(K_1^\ast f\) to belong to \(H\). In fact it belongs to the Hilbert space, because \(K_1^\ast\in L(H)\). But the explanation could be used for relation (36).
reviewed by: Niloufar Seddighi
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 6957371
Wikidata QID: Q59122236
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/3783456
OpenAlex ID: W2255914713
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description: scientific article; zbMATH DE number 6957371