Banach Journal of Mathematical Analysis

Duality properties for generalized frames

F. Enayati and M. S. Asgari

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Abstract

We introduce the concept of Riesz-dual sequences for g-frames. In this paper we show that, for any sequence of operators, we can construct a corresponding sequence of operators with a kind of duality relation between them. This construction is used to prove duality principles in g-frame theory, which can be regarded as general versions of several well-known duality principles for frames. We also derive a simple characterization of a g-Riesz basic sequence as a g-R-dual sequence of a g-frame in the tight case.

Article information

Source
Banach J. Math. Anal. Volume 11, Number 4 (2017), 880-898.

Dates
Received: 22 July 2016
Accepted: 9 December 2016
First available in Project Euclid: 29 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1503993619

Digital Object Identifier
doi:10.1215/17358787-2017-0027

Subjects
Primary: 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 42C15: General harmonic expansions, frames 42C40: Wavelets and other special systems

Keywords
g-orthonormal basis g-frame g-Riesz-dual sequence Riesz duality

Citation

Enayati, F.; Asgari, M. S. Duality properties for generalized frames. Banach J. Math. Anal. 11 (2017), no. 4, 880--898. doi:10.1215/17358787-2017-0027. https://projecteuclid.org/euclid.bjma/1503993619


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