Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules

Rossafi, Mohamed; Eljazzar, Roumaissae; Mohapatra, Ram

doi:10.22130/scma.2023.2001846.1318

Document Type : Research Paper

Authors

¹ LaSMA Laboratory Department of Mathematics Faculty of Sciences, Dhar El Mahraz University Sidi Mohamed Ben Abdellah, Fez, Morocco.

² Laboratory of Partial Differential Equations, Spectral Algebra and Geometry, Department of Mathematics, Faculty Of Sciences, University of Ibn Tofail, Kenitra, Morocco.

³ Department of Mathematics, University of Central Florida, Orlando, FL., 32816, USA.

https://doi.org/10.22130/scma.2023.2001846.1318

Abstract

In the present paper, we introduce the generalized inverse operators, which have an exciting role in operator theory. We establish Douglas' factorization theorem type for the Hilbert pro-$C^{\ast}$-module.We introduce the notion of atomic system and $K$-frame in the Hilbert pro-$C^{\ast}$-module and study their relationship. We also demonstrate some properties of the $K$-frame by using Douglas' factorization theorem.Finally we demonstrate that the sum of two $K$-frames in a Hilbert pro-$C^{\ast}$-module with certain conditions is once again a $K$-frame.

Keywords

Main Subjects

Frame Theory

References

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Sahand Communications in Mathematical Analysis

Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules

References

References

Volume 21, Issue 2
March 2024
Pages 25-49

Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules

References

References

Volume 21, Issue 2March 2024Pages 25-49

Volume 21, Issue 2
March 2024
Pages 25-49