Article ID: MTJPAM-D-24-00026

Title: Weaving continuous generalized frames for operators

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00026; Volume 6 / Issue 1 / Year 2024, Pages 64-73

Document Type: Research Paper

Author(s): Mohamed Rossafi ^a , Hafida Massit ^b , Choonkil Park ^c

^aDepartment of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, Fes, Morocco

^bDepartment of Mathematics, University of Ibn Tofail, Kenitra, Morocco

^cResearch Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Received:13 February 2024, Accepted:26 April 2024, Published:15 May 2024

Corresponding Author: Mohamed Rossafi (Email address: mohamed.rossafi@usmba.ac.ma; mohamed.rossafi@uit.ac.ma)

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Abstract

Recently, Bemrose et al. [2] developed a theory of weaving frames. This theory was motivated by a problem in distributed signal processing. In this article, we introduce the atomic g-system and generalize some known results in continuous L-frames, weaving continuous, and weaving continuous g-frames. Additionally, we study weaving continuous L–g-frames in Hilbert spaces. Moreover, we examine the behavior of continuous L–g-frames under certain perturbations, demonstrating that approximate L-duals are stable under small perturbations. We also show that it is possible to remove elements from a woven continuous L–g-frame and maintain its integrity as a woven frame.

Keywords: Continuous K-frames, continuous g-frames, weaving continuous K–g-frames, perturbation

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