Some characterizations of Banach lattices with the Schur property.

Wnuk, Witold. "Some characterizations of Banach lattices with the Schur property.." Revista Matemática de la Universidad Complutense de Madrid 2.SUPL. (1989): 217-224. <http://eudml.org/doc/43509>.

@article{Wnuk1989,
abstract = {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 l1 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},
author = {Wnuk, Witold},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Estructuras reticulares; equivalence of the Schur and Dunford-Pettis properties in the class of discrete KB-spaces; operator characterization of the Schur property; AL- space},
language = {eng},
number = {SUPL.},
pages = {217-224},
title = {Some characterizations of Banach lattices with the Schur property.},
url = {http://eudml.org/doc/43509},
volume = {2},
year = {1989},
}

TY - JOUR
AU - Wnuk, Witold
TI - Some characterizations of Banach lattices with the Schur property.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1989
VL - 2
IS - SUPL.
SP - 217
EP - 224
AB - 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 l1 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
LA - eng
KW - Estructuras reticulares; equivalence of the Schur and Dunford-Pettis properties in the class of discrete KB-spaces; operator characterization of the Schur property; AL- space
UR - http://eudml.org/doc/43509
ER -