# Duality and biorthogonality for g-frames in Hilbert spaces

Volume 17, Issue 2, pp 220-234 Publication Date: June 15, 2017

### 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.

### Keywords

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

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