Full paper in PDF:
$% W. Wnuk, Some characterizations of Banach lattices with the Schur
property,
Rev. Mat. Univ. Complut. Madrid 2 (1989), supplementary, 217–224.%$
Some Characterizations of Banach Lattices with the Schur Property
This note contains a short proof of the equivalence of the Schur and
Dunford-Pettis properties in the class of discrete KB-spaces. We also present an
operator characterization of the Schur property (Theorem 2) and we notice that
Banach lattices which band hereditary
coincide with Banach lattices having
the Schur property. (This characterization is due to Popa (1977).) Moreover, the
paper offers examples of Banach lattices with the positive Schur property and
without the Schur property and which are not isomorphic to any AL-space.
1980 Mathematics Subject Classification (1985 revision): 46B30, 47B55, 47D15.