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Weak compactness of almost L-weakly and almost M-weakly compact operators


Farid Afkir
Khalid Bouras
Aziz Elbour
Safae El Filali

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.





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eISSN: 1727-933X
print ISSN: 1607-3606