Related papers: Collective order boundedness of sets of operators …
Collective versions of order convergences and corresponding types of collectively qualified sets of operators in vector lattices are investigated. It is proved that collectively order to norm bounded sets are bounded in the operator norm…
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 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 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 develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple…
In this paper, we describe a way of turning a seminormed preordered vector space into an Archimedean order unit space. We show that this construction satisfies a universal property similar to that of the Archimedeanization of Paulsen and…
In an Archimedean directed partially ordered vector space $X$ one can define the concept of a band in terms of disjointness. Bands can be studied by using a vector lattice cover $Y$ of $X$. If $X$ has an order unit, $Y$ can be represented…
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 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…
It is proved that equi-bounded on order intervals families of semi-norms on an ordered Banach space with a closed generating cone are equi-continuous.
Relatively uniformly continuous (ruc) semigroups were recently introduced and studied by Kandi\'c, Kramar-Fijav\v{z}, and the second-named author, in order to make the theory of one-parameter operator semigroups available in the setting of…
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…
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…
Suppose $X$ is a locally solid vector lattice. In this paper, we introduce the notion "$AM$-property" in $X$ as an extension for $AM$-spaces in the category of all Banach lattices. With the aid of this concept, we characterize spaces in…
This paper investigates the boundedness of a broad class of operators within the framework of generalized Morrey-Banach function spaces. This class includes multilinear operators such as multilinear $\omega$-Calder\'{o}n-Zygmund operators,…
We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. We explain how this perspective has several…
We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices,…
We present a systematic development of inductive limits in the categories of ordered *-vector spaces, Archimedean order unit spaces, matrix ordered spaces, operator systems and operator C*-systems. We show that the inductive limit…
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,…
A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of…