On the categories and
We describe the geometric structure of the -characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.
In this paper, we introduce and study new concepts of b-L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of KB-spaces.
We introduce a new class of operators that generalizes L-weakly compact operators, which we call order almost L-weakly compact. We give some characterizations of this class and we show that this class of operators satisfies the domination problem.
We characterize Banach lattices and on which the adjoint of each operator from into which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if and are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator from into has an adjoint Dunford-Pettis operator from into if, and only if, the norm of is order continuous or has the Schur property. As a consequence we show that, if and are two Banach...
In this paper, we introduce and study the class of almost weak Dunford-Pettis operators. As consequences, we derive the following interesting results: the domination property of this class of operators and characterizations of the wDP property. Next, we characterize pairs of Banach lattices for which each positive almost weak Dunford-Pettis operator is almost Dunford-Pettis.
We introduce and study the disjoint weak -convergent operators in Banach lattices, and we give a characterization of it in terms of sequences in the positive cones. As an application, we derive the domination and the duality properties of the class of positive disjoint weak -convergent operators. Next, we examine the relationship between disjoint weak -convergent operators and disjoint -convergent operators. Finally, we characterize order bounded disjoint weak -convergent operators in terms...