Annals of Functional Analysis

G-frames and their generalized multipliers in Hilbert spaces

Hessam Hosseinnezhad, Gholamreza Abbaspour Tabadkan, and Asghar Rahimi

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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.

Article information

Source
Ann. Funct. Anal., Volume 10, Number 2 (2019), 180-195.

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1548126085

Digital Object Identifier
doi:10.1215/20088752-2018-0017

Mathematical Reviews number (MathSciNet)
MR3941380

Zentralblatt MATH identifier
07083887

Subjects
Primary: 42C15: General harmonic expansions, frames
Secondary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

Keywords
g-Bessel sequences g-frames g-Riesz bases generalized multipliers

Citation

Hosseinnezhad, Hessam; Abbaspour Tabadkan, Gholamreza; Rahimi, Asghar. G-frames and their generalized multipliers in Hilbert spaces. Ann. Funct. Anal. 10 (2019), no. 2, 180--195. doi:10.1215/20088752-2018-0017. https://projecteuclid.org/euclid.afa/1548126085


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