Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 7, Number 2 (2013), 172 -193 .
Frames and Riesz bases for Banach spaces, and Banach spaces of vector-valued sequences
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.
Banach J. Math. Anal., Volume 7, Number 2 (2013), 172 -193 .
First available in Project Euclid: 20 March 2013
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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