相关论文: Convergence structures and Hausdorff uo-Lebesgue t…

In this paper we consider the relationship between order and topology in the vector lattice $C_b(X)$ of all bounded continuous functions on a Hausdorff space $X$. We prove that the restriction of $f\in C_b(X)$ to a closed set $A$ induces an…

A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and…

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…

The main aim of the present note is to consider bounded orthomorphisms between locally solid vector lattices. We establish a version of the remarkable Zannen theorem regarding equivalence between orthomomorphisms and the underlying vector…

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,…

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…

We investigate properties of order continuous operators on pre-Riesz spaces with respect to the embedding of the range space into a vector lattice cover or, in particular, into its Dedekind completion. We show that order continuity is…

We study uO convergence on infinitely distributive lattices, extending key properties known from Riesz spaces. We show that order continuity of uO convergence characterizes infinite distributivity. We examine O-adherence and uO adherence of…

Let $E$ be a sublattice of a vector lattice $F$. A continuous operator $T$ from the vector lattice $E$ into a normed vector space $X$ is said to be $\tilde{o}$rder-norm continuous whenever $x_\alpha\xrightarrow{Fo}0$ implies…

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…

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.

A net $(x_\alpha)$ in a vector lattice $X$ is said to uo-converge to $x$ if $|x_\alpha-x|\wedge u\xrightarrow{\rm o}0$ for every $u\ge 0$. In the first part of this paper, we study some functional-analytic aspects of uo-convergence. We…

Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…

Suppose $X$ is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on $X$. In this paper, we consider some situations under which these classes of bounded operators form locally…

Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…

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 study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the…

While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…

Different notions for order convergence have been considered by various authors. Associated to every notion of order convergence corresponds a topology, defined by taking as the closed sets those subsets of the poset satisfying that no net…

For an arbitrary topological space $X$, assume that $S(X)$ is the vector lattice of all equivalence classes of real-valued continuous functions on open dense subsets of $X$; it is a laterally complete vector lattice but not a normed…