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

  • Farid Afkir
  • Khalid Bouras
  • Aziz Elbour
  • Safae El Filali
Keywords: Almost L-weakly compact operator, almost M-weakly compact operator, M- weakly compact operator, L-weakly compact operator, Banach lattice, order continuous norm.


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.


Journal Identifiers

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