L-weakly and M-weakly demicompact operators on Banach lattices-Reference-Cited by-同舟云学术

L-weakly and M-weakly demicompact operators on Banach lattices

Published:2022 Issue:13 Volume:36 Page:4319-4329
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Benkhaled Hedi¹,Hajji Mohamed²,Jeribi Aref¹

Affiliation:

1. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Sfax, Tunisia

2. Department of Mathematics and Computer Science, Issat Kasserine, Kasserine, Tunisia

Abstract

In this paper, we introduce and investigate new concepts of L-weakly and M-weakly demicompact operators. Let E be a Banach lattice. An operator T : E ? E is called L-weakly demicompact, if for every norm bounded sequence (xn) in BE such that {xn ? Txn, n ? N} is an L-weakly compact subset of E, we have {xn, n ? N} is an L-weakly compact subset of E. Additionally, an operator T : E ? E is called M-weakly demicompact if for every norm bounded disjoint sequence (xn) in E such that ?xn ?Txn? ? 0, we have ?xn? ? 0. L-weakly (resp. M-weakly) demicompact operators generalize known classes of operators which are L-weakly (resp. M-weakly) compact operators. We also elaborate some properties of these classes of operators.

Publisher

National Library of Serbia

Subject

General Mathematics

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