Banach Journal of Mathematical Analysis

Duality properties for generalized frames

F. Enayati and M. S. Asgari

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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

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

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

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Zentralblatt MATH identifier

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

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


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.

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