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Weak compactness of almost L-weakly and almost M-weakly compact operators.
- Source :
-
QM - Quaestiones Mathematicae . Oct 2021, Vol. 44 Issue 9, p1145-1154. 10p. - Publication Year :
- 2021
-
Abstract
- In this paper, we investigate conditions on a pair of Banach lattices E and F that tells us when every positive almost L-weakly compact (resp. almost M- weakly compact) operator T : E → F is weakly compact. Also, we present some necessary conditions that tells us when every weakly compact operator T : E → F is almost M-weakly compact (resp. almost L-weakly compact). In particular, we will prove that if every weakly compact operator from a Banach lattice E into a Banach space X is almost L-weakly compact, then E is a KB-space or X has the Dunford-Pettis property and the norm of E is order continuous. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMPACT operators
*BANACH lattices
*COMMERCIAL space ventures
*BANACH spaces
Subjects
Details
- Language :
- English
- ISSN :
- 16073606
- Volume :
- 44
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- QM - Quaestiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 153120180
- Full Text :
- https://doi.org/10.2989/16073606.2020.1777482