\(g\)-bases in Hilbert spaces
type: Item
instance of: scholarly article
title: \(g\)-bases in Hilbert spaces
zbMATH Open document ID: 1266.46018
DOI: 10.1155/2012/923729
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: The concept of \(g\)-bases in Hilbert spaces is introduced, which generalizes Schauder bases in Hilbert spaces. Some results about \(g\)-bases are proved. In particular, we characterize the \(g\)-bases and \(g\)-orthonormal bases. Dual \(g\)-bases are also discussed. We also consider the equivalent relations of \(g\)-bases and \(g\)-orthonormal bases. The property of \(g\)-minimality of \(g\)-bases is studied as well. Our results show that, in some cases, \(g\)-bases share many useful properties of Schauder bases in Hilbert spaces.
Mathematics Subject Classification ID: 46C05
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 6134194
zbMATH Keywords: \(g\)-bases
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: Schauder bases
Wikidata QID: Q58697099
author: Xunxiang Guo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/923729
OpenAlex ID: W1967258731
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description: scientific article; zbMATH DE number 6134194