Decompositions of \(g\)-frames and duals and pseudoduals of \(g\)-frames in Hilbert spaces
type: Item
instance of: scholarly article
title: Decompositions of \(g\)-frames and duals and pseudoduals of \(g\)-frames in Hilbert spaces
zbMATH Open document ID: 1339.46009
DOI: 10.1155/2015/305961
published in: Journal of Function Spaces
publication date: 2015-08-20T00:00:00Z
review text: Summary: Firstly, we study the representation of \(g\)-frames in terms of linear combinations of simpler ones such as \(g\)-orthonormal bases, \(g\)-Riesz bases, and normalized tight \(g\)-frames. Then, we study the dual and pseudodual of \(g\)-frames, which are critical components in reconstructions. In particular, we characterize the dual \(g\)-frames in a constructive way; that is, the formulae for dual \(g\)-frames are given. We also give some \(g\)-frame like representations for pseudodual \(g\)-frame pairs. The operator parameterizations of \(g\)-frames and decompositions of bounded operators are the key tools to prove our main results.
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 6474196
zbMATH Keywords: \(g\)-frames
zbMATH Keywords: dual \(g\)-frames
author: Xunxiang Guo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/305961
OpenAlex ID: W2066374976
Wikidata QID: Q59112792
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description: scientific article; zbMATH DE number 6474196