Related papers: Weak Unbounded Norm Topology and Dounford-Pettis O…

We give a positive answer to the question of K. Bouras [`Almost Dunford-Pettis sets in Banach lattices', \textit{Rend. Circ. Mat. Palermo (2)} \textbf{ 62} (2013), 227--236] concerning weak compactness of almost Dunford-Pettis sets in…

A net $(x_\alpha)$ in a vector lattice $X$ is said to be {unbounded order convergent} (or uo-convergent, for short) to $x\in X$ if the net $(\abs{x_\alpha-x}\wedge y)$ converges to 0 in order for all $y\in X_+$. In this paper, we study…

We study order-to-weak continuous operators from an ordered Banach space to a normed space. It is proved that under rather mild conditions every order-to-weak continuous operator is bounded.

We prove that in a certain class E of nonseparable Banach spaces the norm topology of the dual ball is definable in terms of its weak* topology. Thus, any weak* homeomorphism between duals balls of spaces in E is automatically…

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 paper, we present some necessary and sufficient conditions for semi-compact operators being almost L-weakly compact (resp. almost M-weakly compact) and the converse. Mainly, we prove that if $X$ is a nonzero Banach space, then every…

In this short note, we show that one cannot differentiate between reciprocal Dunford--Pettis sets and V$^*$-sets in a Banach lattice. That is, for a bounded subset $K$ of a Banach lattice $E$, $K$ is a V$^*$-set if and only if $K$ is a…

A continuous operator $T$ between two Banach lattices $E$ and $F$ is called almost order-weakly compact, whenever for each almost order bounded subset $A$ of $E$, $T(A)$ is a relatively weakly compact subset of $F$. In Theorem 4, we show…

In this paper, we continue the investigation of topological properties of unbounded norm (un-)topology in normed lattices. We characterize separability and second countability of un-topology in terms of properties of the underlying normed…

Let $E$ and $F$ be Banach lattices. We show first that the disjointness preserving linear functionals separate the points of any infinite dimensional Banach lattice $E$, which shows that in this case the unbounded disjointness operators…

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 continue the study of dispersed subspaces and disjointly non-singular (DNS) operators on Banach lattices using topological methods. In particular, we provide a simple proof of the fact that in an order continuous Banach lattice an…

We prove that the class of Banach function lattices in which all relatively weakly compact sets are equi-integrable sets (i.e. spaces satisfying the Dunford-Pettis criterion) coincides with the class of 1-disjointly homogeneous Banach…

Recently, J.X. Chen et al. introduced and studied the class of almost limited sets in Banach lattices. In this paper we establish some characterizations of almost limited sets in Banach lattices (resp. wDP* property of Banach lattices),…

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…

We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are…

Several recent papers investigated lattice copies and unbounded convergences in Banach lattices. In this paper, we first solve the problem of RV and LA which is an extension of the well-known James distortion theorem. Using lattice copies…

Recently, the different types of unbounded convergences (uo, un, uaw, uaw*) in Banach lattices were studied. In this paper, we study the continuous functionals with respect to unbounded convergences. We first characterize the continuity of…

Let $ E $ be a space of holomorphic functions on the unit ball $ B_X $ of a Banach space $ X.$ In this work, we introduce a Banach structure associated to $ E $ on the linear space $ WE(Y) $ containing $ Y$-valued holomorphic functions on $…

L- and M-weakly compact operators were introduced by Meyer-Nieberg in the beginning of seventies in attempts of a diversification of the concept of weakly compact operators via imposing Banach lattice structure on the range or on the domain…