We introduce and study the class of positively limited sets in Banach lattices, that is, sets on
which every weak⁎ null sequence of positive functionals converges uniformly to zero …

In the setting of Banach lattices the weak (resp. positive) Grothendieck spaces have been
defined. We localize such notions by defining new classes of sets that we study and …

In this paper, we study some geometric properties in Banach lattices and the class of almost
limited completely continuous operators. For example, we study Banach lattices with …

This paper is devoted to three properties of Banach lattices related to positively limited sets,
which are called the positively limited Schur property of order p (1≤ p≤∞); that is, spaces …

The concept of the strong limited p-Schur property (1⩽ p⩽∞); that is, spaces on which every
weakly p-compact and almost limited set is relatively compact is introduced and studied …

This paper is devoted to two classes of operators related to positively limited sets on Banach
lattices, which we call positively limited operators and positively limited completely …

We characterize the positive Schur property in the positive projective tensor products of
Banach lattices, we establish the connection with the weak operator topology and we give …

We prove the following results:(i) Every absolutely weakly compact set in a Banach lattice is
absolutely weakly sequentially compact.(ii) The converse of (i) holds if $ E $ is separable or …

We study the class of Banach lattices that are positively polynomially Schur. Plenty of
examples and counterexamples are provided, lattice properties of this class are proved …

In this paper we study the norm-attainment of positive operators between Banach lattices. By
considering an absolute version of James boundaries, we prove that: If $ E $ is a reflexive …