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May 2019 G-frames and their generalized multipliers in Hilbert spaces
Hessam Hosseinnezhad, Gholamreza Abbaspour Tabadkan, Asghar Rahimi
Ann. Funct. Anal. 10(2): 180-195 (May 2019). DOI: 10.1215/20088752-2018-0017

Abstract

In this article, we introduce the concept of generalized multipliers for g-frames. In fact, we show that every generalized multiplier for g-Bessel sequences is a generalized multiplier for the induced sequences, in a special sense. We provide some sufficient and/or necessary conditions for the invertibility of generalized multipliers. In particular, we characterize g-Riesz bases by invertible multipliers. We look at which perturbations of g-Bessel sequences preserve the invertibility of generalized multipliers. Finally, we investigate how to find a matrix representation of operators on a Hilbert space using g-frames, and then we characterize g-Riesz bases and g-orthonormal bases by applying such matrices.

Citation

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Hessam Hosseinnezhad. Gholamreza Abbaspour Tabadkan. Asghar Rahimi. "G-frames and their generalized multipliers in Hilbert spaces." Ann. Funct. Anal. 10 (2) 180 - 195, May 2019. https://doi.org/10.1215/20088752-2018-0017

Information

Received: 10 April 2018; Accepted: 17 July 2018; Published: May 2019
First available in Project Euclid: 22 January 2019

zbMATH: 07083887
MathSciNet: MR3941380
Digital Object Identifier: 10.1215/20088752-2018-0017

Subjects:
Primary: 42C15
Secondary: 41A58, 47A05

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 2 • May 2019
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