Characterizing R-duality in Banach spaces
type: Item
instance of: scholarly article
title: Characterizing R-duality in Banach spaces
zbMATH Open document ID: 1268.42054
author: Ole Christensen
author: Xiangchun Xiao
author: Yucan Zhu
publication date: 2013-03-19T00:00:00Z
review text: In [J. Fourier Anal. Appl. 10, No. 4, 383--408 (2004; Zbl 1058.42020)], \textit{P. G. Casazza} et al. introduced the notion of Riesz-dual (R-dual) of some sequences in Hilbert spaces. They also gave some interesting properties of R-dual sequences as an attempt to generalize the duality principle from Gabor analysis to general frames in Hilbert spaces. In [J. Fourier Anal. Appl. 17, No. 4, 640--655 (2011; Zbl 1222.42031)], the first author et al. gave new characterizations of R-duality in Hilbert spaces and several examples. On the other hand, the two last authors [Acta Math. Sci., Ser. A, Chin. Ed., 29, No. 1, 94--102 (2009; Zbl 1199.42137)] extended R-duality to Banach spaces. In the present paper, the authors give some new characterizations of R-dual sequences in Banach spaces.
reviewed by: Paşc Găvruţă
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 6146288
zbMATH Keywords: R-dual
zbMATH Keywords: p-frames
MaRDI profile type: Publication
full work available at URL: s10114-012-1199-4
OpenAlex ID: W2021227255
cites work: Duality principles in frame theory
cites work: On the duality principle by Casazza, Kutyniok, and Lammers
cites work: Q3405229
cites work: \(p\)-frames in separable Banach spaces
cites work: \(q\)-Besselian frames in Banach spaces
cites work: Q3955832
cites work: Q3966611
DOI: 10.1007/S10114-012-1199-4
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6146288