Related papers: Generalizations of L- and M-weakly compact operato…

The goal of this note is two-fold. First we present a brief overview of "weak" embeddings, with a special emphasis on sign embeddings which were introduced by H. P. Rosenthal in the early 1980s. We also discuss the related notion of narrow…

In this paper, considering a real Banach sequence lattice Y instead of a Lebesgue sequence space $l_p$ we generalize p-convexity of a linear operator $T:E\to X$, where E is a Banach space and X is a Banach lattice. Then we prove that basic…

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…

In this paper, we introduce and study a new classes of operators, named AM-unbounded norm compact operators. We study the the basic properties of the new operator and we investigate the lattice-order and topology property of the operator…

We introduce and study the class of weak almost limited operators. We establish a characterization of pairs of Banach lattices $E$, $F$ for which every positive weak almost limited operator $T:E\rightarrow F$ is almost limited (resp. almost…

A. Bahramnezhad and K. Haghnejad Azar introduced the classes of $KB$-operators and $WKB$-operators, and they studied some of theirs properties. In the present paper, we give answer for an open problem from that paper, which two…

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the…

We investigate more closely the class of generalized b-weakly compact operators on locally convex-solid Riesz spaces and we provide new sequential and operator characterizations in relation with the subject. We introduce explicitly the…

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…

Let $X$ and $Y$ be separable Banach spaces. Suppose $Y$ either has a shrinking basis or $Y$ is isomorphic to $C(2^\mathbb{N})$ and $A$ is a subset of weakly compact operators from $X$ to $Y$ which is analytic in the strong operator…

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…

In this paper, using the concept of unbounded absolute weak convergence ($uaw$-convergence, for short) in a Banach lattice, we define two classes of continuous operators, named $uaw$-Dunford-Pettis and $uaw$-compact operators. We…

Let $p\in[1,\infty]$. Being motivated by weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly $p$-convergent and weak$^\ast$…

The paper is devoted to the relationship between almost limited operators and weakly compacts operators. We show that if $F$ is a $\sigma $-Dedekind complete Banach lattice then, every almost limited operator $T:E\rightarrow F $ is weakly…

We investigate the duality and norm completeness in the classes of limitedly--L-weakly compact and Dunford--Pettis--L-weakly compact and operators from Banach spaces to Banach lattices.

This paper deals with the problem of when, given a collection $\mathcal C$ of weakly compact operators between separable Banach spaces, there exists a separable reflexive Banach space $Z$ with a Schauder basis so that every element in…

In the present paper, we introduce and investigate the multiplicative order compact operators from vector lattices to $l$-algebras. A linear operator $T$ from a vector lattice $X$ to an $l$-algebra $E$ is said to be $\mathbb{omo}$-compact…

Using Mujica's linearization theorem, we extend to the holomorphic setting some classical characterizations of compact (weakly compact, Rosenthal, Asplund) linear operators between Banach spaces such as the Schauder, Gantmacher and…

We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of…

We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.