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Some characterizations of unbounded Dunford–Pettis operators

Part of: Special classes of linear operators Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  15 September 2025

Sanaa Boumnidel ,
Abdelmonaim El Kaddouri Open the ORCID record for Abdelmonaim El Kaddouri [Opens in a new window]  and
Moulay Othman Aboutafail
Sanaa Boumnidel
Affiliation:
Department of Mathematics, Faculty Polydisciplinary of Larache, Abdelmalek Essaadi University , P.O. Box 745, Larache 92004, Morocco e-mail: bsanouaa@gmail.com
Abdelmonaim El Kaddouri*
Affiliation:
Engineering Sciences Laboratory, National School of Applied Sciences (ENSAK), Ibn Tofail University , B.P. 241, Kenitra 14000, Morocco e-mail: moulayothman.aboutafail@uit.ac.ma
Moulay Othman Aboutafail
Affiliation:
Engineering Sciences Laboratory, National School of Applied Sciences (ENSAK), Ibn Tofail University , B.P. 241, Kenitra 14000, Morocco e-mail: moulayothman.aboutafail@uit.ac.ma
*
e-mail: aelkaddouri@uit.ac.ma
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Abstract

We give some characterizations of $\sigma $-unbounded Dunford–Pettis operators (whenever $x_{n}\overset {uaw}{\longrightarrow } 0$ implies that $T(x_{n})\overset {un}{\longrightarrow } 0$). In addition, we study some properties of this operator, some other interesting results are also obtained.

Keywords

uaw-convergenceun-convergenceσ-uaw-compact operatorun-compact operator

MSC classification

Primary: 46B42: Banach lattices 47B60: Operators on ordered spaces 47B65: Positive operators and order-bounded operators

Information

Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 8
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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References

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