Douglas' factorization theorem and atomic system in Hilbert pro-C^∗-module

2022/09/18 by Mohamed Rossafi, Rossafi, Mohamed, Roumaissae Eljazzar +3
Mathematics · #42C15 #46L05 #47A05 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2212.01177

openalex publication_date 2022/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-C^∗-module. We introduce the notion of atomic system and of K-frame in Hilbert pro-C^∗-module and we study the relationship between them. We also demonstrat some properties of K-frame by using Douglas' factorization theorem.Finally we demonstrate that the sum of two K-frames in a Hilbert pro-C^∗-module with certain conditions is once again a K-frame.

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