Some new characterizations and \(g\)-minimality and stability of \(g\)-bases in the Hilbert spaces
type: Item
instance of: scholarly article
title: Some new characterizations and \(g\)-minimality and stability of \(g\)-bases in the Hilbert spaces
zbMATH Open document ID: 1282.46017
DOI: 10.1155/2013/272407
published in: Journal of Function Spaces and Applications
publication date: 2013-07-05T00:00:00Z
review text: Summary: The concept of \(g\)-basis in the Hilbert spaces has been introduced by \textit{X.-X. Guo} [Abstr. Appl. Anal. 2012, Article ID 923729 (2012; Zbl 1266.46018)], generalizing the concept of the Schauder basis in Hilbert spaces. A~\(g\)-basis plays a similar role in \(g\)-frame theory as the Schauder basis plays in frame theory. In the present paper, we establish some important properties of \(g\)-bases in Hilbert spaces. In particular, we obtain a simple condition under which some important properties established by Guo [loc.\,cit.]\ remain true. With these conditions, we also establish some new interesting properties of \(g\)-bases which are related to \(g\)-minimality. Finally, we obtain a perturbation result about \(g\)-bases.
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 46C99
zbMATH DE Number: 6184391
zbMATH Keywords: \(g\)-basis
zbMATH Keywords: Schauder basis
zbMATH Keywords: Hilbert space
Wikidata QID: Q59013902
author: Xunxiang Guo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/272407
OpenAlex ID: W2031418364
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description: scientific article; zbMATH DE number 6184391