Duality and biorthogonality for g-frames in Hilbert spaces

Volume 17, Issue 2, pp 220-234 http://dx.doi.org/10.22436/jmcs.017.02.04

Publication Date: June 15, 2017 Submission Date: September 14, 2016

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Authors

Farideh Enayati - Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran. Mohammad Sadegh Asgari - Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

Abstract

The main aim of this paper is to define the generalized Riesz-dual sequence from a g-Bessel sequence with respect to a pair of g-orthonormal bases. We characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract g-frame setting.

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Keywords

• g-orthonormal basis
• g-frames
• g-Riesz-dual sequence
• Riesz-duality.

MSC

•  41A58
•  42A38
•  42C15
•  42C40

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