Douglas' factorization theorem and atomic system in Hilbert pro$-C^{\ast}-$module
Functional Analysis
2022-12-05 v1
Abstract
In the present paper we introduce the generalized inverse operators which have an interesting role in operator theory. We establish Douglas' factorization theorem type for Hilbert pro--module. We introduce the notion of atomic system and of -frame in Hilbert pro--module and we study the relationship between them. We also demonstrat some properties of -frame by using Douglas' factorization theorem.Finally we demonstrate that the sum of two -frames in a Hilbert pro--module with certain conditions is once again a -frame.
Cite
@article{arxiv.2212.01177,
title = {Douglas' factorization theorem and atomic system in Hilbert pro$-C^{\ast}-$module},
author = {Mohamed Rossafi and Roumaissae Eljazzar and Ram Mohapatra},
journal= {arXiv preprint arXiv:2212.01177},
year = {2022}
}