Some characterizations of Banach lattices with the Schur property.
Wnuk, Witold
Revista Matemática de la Universidad Complutense de Madrid, Tome 2 (1989), p. 217-224 / Harvested from Biblioteca Digital de Matemáticas
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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

Publié le : 1989-01-01
DMLE-ID : 603 
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     title = {Some characterizations of Banach lattices with the Schur property.},
     journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
     volume = {2},
     year = {1989},
     pages = {217-224},
     zbl = {0717.46018},
     mrnumber = {MR1057221},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43509}
}

Wnuk, Witold. Some characterizations of Banach lattices with the Schur property.. Revista Matemática de la Universidad Complutense de Madrid, Tome 2 (1989) pp. 217-224. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43509/