相关论文: Topological algebras of statistical $\tau$-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.

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…

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 give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators.…

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 investigate the $o\tau$-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the KB operators between locally solid lattices and topological vector spaces; and the Levi operators from…

We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $\tau$ strict contractions}, and some…

In this note, we consider the space of all continuous operators with respect to the unbounded topology on locally solid vector lattices. We investigate whether this space forms a band. In addition, we look into some situations under which,…

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

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…

Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…

In this paper, we investigate the relation between the Deddens and spectral radius algebras of two bounded linear operators, noting a similarity between them. Additionally, we characterize the Deddens and spectral radius algebras related to…

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 two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain…

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…

Let $A$ be a partial *-algebra endowed with a topology $\tau$ that makes it into a locally convex topological vector space $A[\tau]$. Then $A$ is called a topological partial *-algebra if it satisfies a number of conditions, which all…

We continue our study of topological partial *algebras, focusing our attention to the interplay between the various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link…

In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the…

We study properties of the topological space of composition operators on the Banach algebra of bounded functions on an unbounded, locally finite metric space in the operator norm topology and essential norm topology. Moreover, we…