Related papers: On automatic boundedness of some operators in orde…
We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.
It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered…
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 continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to…
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…
We consider linear narrow operators on lattice-normed spaces. We prove that, under mild assumptions, every finite rank linear operator is strictly narrow (before it was known that such operators are narrow). Then we show that every…
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…
Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two folded: (i) we provide a set…
We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that…
We present the current results in the study of weighted composition operators on weighted Banach spaces of an unbounded, locally finite metric space. Specifically, we determine characterizations of bounded and compact weighted composition…
In this paper, we investigate the boundedness of composition operators defined on a quasi-Banach space continuously included in the space of smooth functions on a manifold. We prove that the boundedness of a composition operator strongly…
A bounded linear operator between Banach spaces is called {\it completely continuous} if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous…
In this paper, we investigate more about relationship between $uaw$ -convergence (resp. $un$-convergence) and the weak convergence. More precisely, we characterize Banach lattices on which every weak null sequence is $uaw$-null. Also, we…
We obtain sufficient conditions for a densely defined operator on the Fock space to be bounded or compact. Under the boundedness condition we then characterize the compactness of the operator in terms of its Berezin transform.
We answer the question of W.T. Gowers, giving an example of a bounded operator on a subspace of Gowers unconditional space which is not a strictly singular perturbation of a restriction of a diagonal operator. We make some observations on…
For operators representing ill-posed problems, an ordering by ill-posedness is proposed, where one operator is considered more ill-posed than another one if the former can be expressed as a cocatenation of bounded operators involving the…
We introduce an ordinal index which characterizes weak compactness of operators between Banach spaces. We study when classes consisting of operators having bounded index form a closed ideal, the distinctness of the classes, and the…
In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…
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…
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…