Related papers: Collective order convergence and collectively qual…

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…

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.

We characterize vector lattices in which unbounded order convergence is eventually order bounded. Among other things, the characterization provides a solution to \cite[Probl.23]{Az}.

We show that, for a class of locally solid topologies on vector lattices, a topologically convergent net has an embedded sequence that is unbounded order convergent to the same limit. Our result implies, and often improves, many of the…

This is a survey of some recent applications of Boolean valued models of set theory to order bounded operators in vector lattices.

A collectively $\sigma$-Levi set of operators is a generalization of the $\sigma$-Levi operator. By use of collective order convergence, we investigate relations between collectively $\sigma$-Levi and collectively compact sets of operators.

We study relatively uniformly continuous operator semigroups on ordered vector spaces and extend several recent results obtained by M. Kramar Fijavz, M. Kandic, M. Kaplin, and J. Gluck in the vector lattice setting to ordered vector spaces…

We consider vector lattices endowed with locally solid convergence structures, which are not necessarily topological. We show that such a convergence is defined by the convergence to $0$ on the positive cone. Some results on unbounded…

The notion of unboundedly order converges has been recieved recently a particular attention by several authors. The main result of the present paper shows that the notion is efficient and deserves that care. It states that a vector lattice…

In this paper, we introduce statistical bounded set on topological vector space. Also, we consider three classes of bounded operators from topological vector spaces to ordered topological vector spaces. Moreover, we give relations between…

Let $X$ be a vector lattice and $(E,\tau)$ be a locally solid vector lattice. An operator $T:X\to E$ is said to be $ob$-bounded if, for each order bounded set $B$ in $X$, $T(B)$ is topologically bounded in $E$. In this paper, we study on…

Continuum limits of Laplace operators on general lattices are considered, and it is shown that these operators converge to elliptic operators on the Euclidean space in the sense of the generalized norm resolvent convergence. We then study…

A vector sublattice of the order bounded operators on a Dedekind complete vector lattice can be supplied with the convergence structures of order convergence, strong order convergence, unbounded order convergence, strong unbounded order…

This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…

Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of…

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…

Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriate topologies, we show that under some conditions, they…

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…

We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups and partially ordered vector spaces, respectively. An order topology is introduced such that…

The notion of a Levi operator is an operator abstraction of the Levy property of a norm or, more generally of the Levi topology on a locally solid vector lattice. Various aspects of Levi operators have been studied recently by several…