Related papers: Weak compactness of almost limited operators

Let $X$ be a pointed compact metric space. Assuming that $\mathrm{lip}_0(X)$ has the uniform separation property, we prove that every weakly compact composition operator on spaces of Lipschitz functions $\mathrm{Lip}_0(X)$ and…

We consider $C$-compact orthogonally additive operators in vector lattices. After providing some examples of $C$-compact orthogonally additive operators on a vector lattice with values in a Banach space we show that the set of those…

We investigate for a bounded semigroup of linear operators $S$ on a Banach space $E$ and a vector $x \in E$, when relative compactness of $S(I-T)x$ for every $T \in S$ implies relative compactness of the orbit $Sx$. In particular, we derive…

We prove quantitative factorization results for several classes of operators, including weakly compact, Rosenthal, and $\xi$-Banach-Saks operators.

We extend the notion of narrow operators to nonlinear maps on vector lattices. The main objects are orthogonally additive operators and, in particular, abstract Uryson operators. Most of the results extend known theorems obtained by O.…

We show that every Banach space in which weakly compact sets are super weakly compact in automatically weakly sequentially complete answering a question by Silber (2024). In the proof we show how to build a weakly compact set which is not…

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.

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 prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…

Similar to the theory of finite Markov chains it is shown that in a Banach space $X$ ordered by a closed cone $K$ with nonempty interior int($K$) a power bounded positive operator $A$ with compact power such that its trajectories for…

It is known that a positive commutator $C=A B - B A$ between positive operators on a Banach lattice is quasinilpotent whenever at least one of $A$ and $B$ is compact. In this paper we study the question under which conditions a positive…

We explore the relation between lattice versions of strict singularity for operators from a Banach lattice to a Banach space. In particular, we study when the class of disjointly strictly singular operators, those not invertible on the span…

The space Weak L^1 consists of all measurable functions on [0,1] such that q(f) = sup_{c>0} c \lambda{t : |f(t)| > c} is finite, where \lambda denotes Lebesgue measure. Let \rho be the gauge functional of the unit ball {f : q(f) \leq 1} of…

In this paper, we introduce the concept of a pseudo weakly compact operator of order $ p $ between Banach spaces. Also we study the notion of $ p $-Dunford-Pettis relatively compact property which is in "general" weaker than the…

We analyze the properties of weakly compact sets in Lipschitz free spaces. Prior research has established that, for a complete metric space $M$, weakly precompact sets in the Lipschitz free space $\mathcal F(M)$ are tight. In this paper, we…

This paper deals with the notion of weak Lawvere-Tierney topology on a topos. Our motivation to study such a notion is based on the observation that the composition of two Lawvere-Tierney topologies is no longer idempotent, when seen as a…

An action of a group $G$ on a compact space $X$ is called weakly almost periodic if the orbit of every continuous function on $X$ is weakly relatively compact in $C(X)$. We observe that for a topological group $G$ the following are…

We introduce notions of compactness and weak compactness for multilinear maps from a product of normed spaces to a normed space, and prove some general results about these notions. We then consider linear maps $T:A\to B$ between Banach…

We prove that in the setting of operator spaces the result of Davis, Figiel, Johnson and Pelczynski on factoring weakly compact operators holds accordingly. Though not related directly to the main theorem we add a remark on the description…

A Hausdorff topology $\tau$ on the bicyclic monoid with adjoined zero $\mathcal{C}^0$ is called {\em weak} if it is contained in the coarsest inverse semigroup topology on $\mathcal{C}^0$. We show that the lattice $\mathcal{W}$ of all weak…