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Positivity

, Volume 24, Issue 1, pp 141–149 | Cite as

Some properties of almost L-weakly and almost M-weakly compact operators

  • Aziz ElbourEmail author
  • Farid Afkir
  • Mohammed Sabiri
Article
  • 35 Downloads

Abstract

In this paper, we investigate necessary and sufficient conditions under which compact operators between Banach lattices must be almost L-weakly compact (resp. almost M-weakly compact). Mainly, it is proved that if X is a non zero Banach space then every compact operator \(T{:}X\rightarrow E\) (resp. \(T{:}E\rightarrow X\)) is almost L-weakly compact (resp. almost M-weakly compact) if and only if the norm on E (resp. \(E^{\prime }\)) is order continuous. Moreover, we present some interesting connections between almost L-weakly compact and L-weakly compact operators (resp. almost M-weakly compact and M-weakly compact operators).

Keywords

L-weakly compact operator M-weakly compact operator Almost L-weakly compact operator Almost M-weakly compact Order continuous norm Banach lattice 

Mathematics Subject Classification

46B07 46B42 47B50 

Notes

Acknowledgements

The authors would like to thank the referee(s) for helpful comments and suggestions on the first version of the paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences and TechnologiesMoulay Ismaïl UniversityErachidiaMorocco

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