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Reflexivity and the separable quotient problem for a class of Banach spaces

100%

Wójtowicz M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

tom Vol. 50, no 4

383-394

Let E be a Banach lattice and let X be its closed subspace such that: X is complemented in E, or the norm of E is order continuous. Then X is reflexive iff X* contains no isomorphic copy of l1 iff for every n ≥ l, the nth dual X(n) of X contains no isomorphic copy of l1 iff X has no quotient isomorphic to c0 and X does not have a subspace isomorphic to l1 (Theorem 2). This is an extension of the results obtained earlier by Lozanovskiĭ, Tzafriri, Meyer-Nieberg, and Diaz and Fernández. The theorem is applied to show that many Banach spaces possess separable quotients isomorphic to one of the following spaces: c0, l1, or a reflexive space with a Schauder basis.

Exhaustive submeasures on Boolean rings, Banach lattices and uniform absolute continuity

100%

Huff C. , Lewis P.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

tom Vol. 49, no 3

203-210

A bi-sequential version of a classical theorem dealing with uniform absolute continuity in spaces of measures is extended to the setting of submeasures on a Boolean ring. Applications to spaces of vector measures and Banach lattices are discussed.

Weak and almost Dunford-Pettis operators on Banach lattices

100%

Aqzzouz B. , Bouras K.

Demonstratio Mathematica

2013

tom Vol. 46, nr 1

165--179

We introduce the class of Banach lattices with the AM-compactness property and we use it to characterize Banach lattices on which each positive weak Dunford–Pettis operator is almost Dunford–Pettis and conversely.