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2013 Frames and Riesz bases for Banach spaces, and Banach spaces of vector-valued sequences
Kyugeun Cho, Ju Myung Kim, Han Ju Lee
Banach J. Math. Anal. 7(2): 172-193 (2013). DOI: 10.15352/bjma/1363784230

Abstract

This paper is devoted to an investigation of frames and Riesz bases for general Banach sequence spaces. We establish various relationships between Bessel (respectively, frames) and Riesz sequences (respectively, Riesz bases), and then some of their applications are presented. Some recent results for Banach frames and atomic decompositions are sharpened with simple proofs. Banach spaces consisting of Bessel or Riesz sequences are introduced and it is shown that they are isometrically isomorphic to some Banach spaces of bounded linear operators, and that some subspaces of those Banach spaces are isometrically isomorphic to some Banach spaces of compact operators.

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Kyugeun Cho. Ju Myung Kim. Han Ju Lee. "Frames and Riesz bases for Banach spaces, and Banach spaces of vector-valued sequences." Banach J. Math. Anal. 7 (2) 172 - 193, 2013. https://doi.org/10.15352/bjma/1363784230

Information

Published: 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1271.46013
MathSciNet: MR3039946
Digital Object Identifier: 10.15352/bjma/1363784230

Subjects:
Primary: 46B15
Secondary: 46B28 , 46B45

Keywords: ‎approximation property‎‎ , atomic decomposition , Banach sequence space , frame , Riesz basis

Rights: Copyright © 2013 Tusi Mathematical Research Group

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Vol.7 • No. 2 • 2013
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