Related papers: AM-unbounded norm compact operators on Banach latt…
We introduce the class of unbounded $M$-weakly operators and the class of unbounded $L$-weakly compact operators. We investigate some properties for these new classification of operators and we study relation between them and $M$-weakly…
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,…
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.
Several recent papers investigated unbounded convergences in Banach lattices. Combine all unbounded convergences, including unbounded order (norm, absolute weak, absolute weak*) convergence, we characterize L-weakly compact sets, L-weakly…
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…
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 (…
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…
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…
We study properties of the topological space of composition operators on the Banach algebra of bounded functions on an unbounded, locally finite metric space in the operator norm topology and essential norm topology. Moreover, we…
Based on the concept of unbounded absolutely weakly convergence, we give new characterizations of L-weakly compact sets. As applications, we find some properties of order weakly compact operators. Also, a new characterizations of order…
Recently, the functionals different types of unbounded convergences (uo, un, uaw, uaw*) in Banach lattices were studied. In this paper, we study the continuous operators with respect to unbounded convergences. We first investigate the…
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.…
In this paper, we introduce and study a new concept of unbounded order demi Dunford-Pettis operators. Namely, we investigate some properties for this new class of operators and we study its connection with other known operators, we also…
We introduce new class of limitedly L-weakly compact operators from a Banach space to a Banach lattice. This class is a proper subclass of the Bourgain-Diestel operators and it contains properly the class of L-weakly compact operators. We…
We study composition operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm and the essential norm. In addition, we study the isometric…
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.
We study almost L(M) weakly compact and order L(M) weakly compact operators in Banach spaces. Several further topics related to these operators are investigated.
In this paper, we study $un$-dual (in symbol, $\ud{E}$) of Banach lattice $E$ and compare it with topological dual $E^*$. If $E^*$ has order continuous norm, then $E^* = \ud{E}$. We introduce and study weakly unbounded norm topology…
We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded…
This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…