We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).
We establish some properties of the class of order weakly compact operators on Banach lattices. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms.
Let be a real Banach space and let be an ideal of over a -finite measure space . Let be the space of all strongly -measurable functions such that the scalar function , defined by for , belongs to . The paper deals with strong topologies on . In particular, the strong topology ( the order continuous dual of ) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.
In this article, it will be shown that every -subgroup of a Specker -group has singular elements and that the class of -groups that are -subgroups of Specker -group form a torsion class. Methods of adjoining units and bases to Specker -groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker -group.