## Banach Journal of Mathematical Analysis

### Frames and Riesz bases for Banach spaces, and Banach spaces of vector-valued sequences

#### 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.

#### Article information

Source
Banach J. Math. Anal., Volume 7, Number 2 (2013), 172 -193 .

Dates
First available in Project Euclid: 20 March 2013

https://projecteuclid.org/euclid.bjma/1363784230

Digital Object Identifier
doi:10.15352/bjma/1363784230

Mathematical Reviews number (MathSciNet)
MR3039946

Zentralblatt MATH identifier
1271.46013

Subjects
Primary: 46B15
Secondary: 46B28 46B45

#### Citation

Cho, Kyugeun; Kim, Ju Myung; Lee, Han Ju. Frames and Riesz bases for Banach spaces, and Banach spaces of vector-valued sequences. Banach J. Math. Anal. 7 (2013), no. 2, 172 --193. doi:10.15352/bjma/1363784230. https://projecteuclid.org/euclid.bjma/1363784230

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