On Some Fixed Point Principles for Cones in Linear Normed Spaces.
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.
Let be an Archimedean -group. We denote by and the divisible hull of and the distributive radical of , respectively. In the present note we prove the relation . As an application, we show that if is Archimedean, then it is completely distributive if and only if it can be regularly embedded into a completely distributive vector lattice.
We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.
In this note we prove that there exists a Carathéodory vector lattice such that and . This yields that is a solution of the Schröder-Bernstein problem for Carathéodory vector lattices. We also show that no Carathéodory Banach lattice is a solution of the Schröder-Bernstein problem.