Related papers: Operators Affiliated to Banach Lattice Properties …
Suppose $E$ is a Banach lattice. Recently, there have been some motivating contexts regarding the known Banach-Saks property and the Grothendieck property from an order point of view. In this paper, we establish these results for operators…
This paper introduces and investigates novel properties of uaw-Dunford-Pettis operators on Banach spaces, exploring their relationships with other classes of operators. We further define and characterize new property of Banach lattices.…
We introduce and study the enveloping norms of regularly P-operators, where P is an "almost" version of limited, Grothendieck, and of Dunford--Pettis operators in Banach lattices. Several further topics related to these operators are also…
We study operators carrying disjoint bounded subsets of a Banach lattice into compact, weakly compact, and limited subsets of a Banach space. Surprisingly, these operators behave differently with classical compact, weakly compact, and…
We study (almost) limited operators in Banach lattices and their relations to L-weakly compact, semi-compact, and Dunford-Pettis operators. Several further related topics are investigated.
Recently, J. H'michane et al. introduced the class of weak* Dunford-Pettis operators on Banach spaces, that is, operators which send weakly compact sets onto limited sets. In this paper the domination problem for weak* Dunford-Pettis…
Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce two types of continuous operators between Banach lattices using unbounded absolute weak convergence. We…
In this paper we introduce and study a new class of operators related to norm bounded sets on Banach Lattice and which brings together several classical classes of operators (as o-weakly compact operators, b-weakly compact operators,…
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 the property (d) and we give a new characterization of this…
This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call $DW$-DP operators and $DW$-limited operators, respectively. They carry disjointly weakly compact subsets of a Banach…
We introduce a class of operators which is called unbounded Dunford-Pettis. In this paper, we study some properties of the operators, relationships with the other classes of operators and the space of these operators.
Given a Banach lattice $L,$ the space of lattice Lipschitz operators on $L$ has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is…
Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce unbounded continuous operators by replacing weak convergence with the unbounded absolutely weak convergence (…
First we characterize the Banach lattices E whose biduals have the positive Schur property by means of second adjoints of operators on E being almost Dunford-Pettis. Next we extend some known results concerning conditions on the Banach…
In this paper, we characterize Banach lattices on which each Dunford-Pettis operator (or weak Dunford-Pettis) is unbounded absolute weak Dunford-Pettis operator and the converse.
This paper is devoted to the study of $DW$-compact operators, that is, those operators which map disjointly weakly compact sets in a Banach lattice onto relatively compact sets. We show that $DW$-compact operators are precisely the…
In this article, the class of all Dunford-Pettis $ p $-convergent operators and $ p $-Dunford-Pettis relatively compact property on Banach spaces are investigated. Moreover, we give some conditions on Banach spaces $ X $ and $ Y $ such that…
In this note, we consider several notions related to the Grothendieck property. Among them, we introduce the notion "unbounded Grothendieck property" in a Banach lattice as an unbounded version of the known Grothedieck property in the…
Suppose $X$ is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on $X$. In this paper, we consider some situations under which these classes of bounded operators form locally…
In this paper, we will study some properties of b-weakly compact operators and we will investigate their relationships to some variety of operators on the normed vector lattices. With some new conditions, we show that the modulus of an…