Weak limited sets and operators on Banach lattices

  • Farid Afkir
  • Aziz Elbour
Keywords: Weak limited set, weakly precompact set, weak limited operator, Dunford- Pettis operator, Banach lattice, order continuous norm.


In this paper, we prove that an operator T : EF, between two Banach lattices, maps order intervals onto weak limited sets if and only if the modulus jSTj exists and is Dunford-Pettis for every Dunford-Pettis operator S : F → c0. Next, we establish that a Banach lattice E does not contain any isomorphic copy of ℓ1 if and only if the order intervals of E are weak limited and the norm of E′ is order continuous. We also investigate the domination problem of the class of weak limited operators.


Journal Identifiers

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