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November 2019 Generalized frames for controlled operators in Hilbert spaces
Dongwei Li, Jinsong Leng
Ann. Funct. Anal. 10(4): 537-552 (November 2019). DOI: 10.1215/20088752-2019-0012

Abstract

Controlled frames and g-frames were considered recently as generalizations of frames in Hilbert spaces. In this paper we generalize some of the known results in frame theory to controlled g-frames. We obtain some new properties of controlled g-frames and obtain new controlled g-frames by considering controlled g-frames for its components. And we also find some new resolutions of the identity. Furthermore, we study the stabilities of controlled g-frames under small perturbations.

Citation

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Dongwei Li. Jinsong Leng. "Generalized frames for controlled operators in Hilbert spaces." Ann. Funct. Anal. 10 (4) 537 - 552, November 2019. https://doi.org/10.1215/20088752-2019-0012

Information

Received: 15 October 2018; Accepted: 7 February 2019; Published: November 2019
First available in Project Euclid: 30 October 2019

zbMATH: 07126071
MathSciNet: MR4026367
Digital Object Identifier: 10.1215/20088752-2019-0012

Subjects:
Primary: 42C15
Secondary: 47B99

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 4 • November 2019
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