Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 10, Number 2 (2019), 180-195.
G-frames and their generalized multipliers in Hilbert spaces
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.
Ann. Funct. Anal., Volume 10, Number 2 (2019), 180-195.
Received: 10 April 2018
Accepted: 17 July 2018
First available in Project Euclid: 22 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
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