Open Access
October 2017 Duality properties for generalized frames
F. Enayati, M. S. Asgari
Banach J. Math. Anal. 11(4): 880-898 (October 2017). DOI: 10.1215/17358787-2017-0027


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.


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F. Enayati. M. S. Asgari. "Duality properties for generalized frames." Banach J. Math. Anal. 11 (4) 880 - 898, October 2017.


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

zbMATH: 06841259
MathSciNet: MR3708534
Digital Object Identifier: 10.1215/17358787-2017-0027

Primary: 41A58 , 42A38
Secondary: 42C15 , ‎42C40

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

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 4 • October 2017
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