On the Restrictions of Weakly Demicompact Operators and Generalized Fredholm Theory

The purpose of this paper is to explore the weak demicompactness of the operator $T_n$, which is the restriction of a linear operator $T$ to its range $\mathcal{R}(T^n)$, $T_n$ are considered as linear operators from $\mathcal{R}(T^n)$ to itself, $n\in\mathbb{N}$. As well, we present several results...

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Bibliographic Details
Date:2026
Main Authors: Kchaou, Omaima, Krichen, Bilel
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2026
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Online Access:https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1126
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Journal Title:Journal of Mathematical Physics, Analysis, Geometry

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Journal of Mathematical Physics, Analysis, Geometry
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Summary:The purpose of this paper is to explore the weak demicompactness of the operator $T_n$, which is the restriction of a linear operator $T$ to its range $\mathcal{R}(T^n)$, $T_n$ are considered as linear operators from $\mathcal{R}(T^n)$ to itself, $n\in\mathbb{N}$. As well, we present several results on upper generalized semi-Fredholm operators, focusing on the concept of weak demicompact operators. We specify conditions on certain ranges that ensure the persistence of the weak demicompactness property under restrictions. Moreover, our study provides perturbation results concerning the generalized Gustafson essential spectrum for $2\times 2$ operator matrices. Mathematical Subject Classification 2020: 47A53, 47A10