Related papers: On Levi operators between normed and vector lattic…
Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a…
The paper is devoted to establishing relationships between global and local monotonicity, as well as their maximality versions, for single-valued and set-valued mappings between finite-dimensional and infinite-dimensional spaces. We first…
This paper considers averaging operators on various algebraic structures and studies the induced structures. We first introduce the notion of an averaging operator on a group $G$ and show that it induces a rack structure. Moreover, the…
Given a countable dense subset D of an infinite-dimensional separable Hilbert space H the set of operators for which every vector in D except zero is hypercyclic (weakly supercyclic) is residual for the strong (resp. weak) operator topology…
We prove that if any $\lfloor3d/2 \rfloor$ or fewer elements of a finite family of linear operators $\mathbb K^d\to \mathbb K^d$ ($\mathbb K$ is an arbitrary field) have a common eigenvector then all operators in the family have a common…
We investigate the representation of lattices as sublattices of the lattice of all convex subsets (intervals) of a linearly ordered set $(X,\le)$. We introduce the purely lattice-theoretic notion of a \textit{loc-lattice} and prove that…
For every closed subset $X$ of a stratifiable [resp. metrizable] space $Y$ we construct a positive linear extension operator $T:R^{X\times X}\to R^{Y\times Y}$ preserving constant functions, bounded functions, continuous functions,…
We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.
We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$. The last ones are connected with Hardy-Orlicz and…
Two kinds of differential operators that can be generally defined on an arbitrary smooth surface in a finite dimensional Euclid space are studied, one is termed as surface gradient and the other one as Levi-Civita gradient. The surface…
A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. We define a class of bases called…
Let $X$ be a complex topological vector space and $L(X)$ the set of all continuous linear operators on $X.$ In this paper, we extend the notion of the codiskcyclicity of a single operator $T\in L(X)$ to a set of operators $\Gamma\subset…
We characterize a weighted norm inequality which corresponds to the embedding of a class of absolutely continuous functions into the fractional order Sobolev space. The auxiliary result of the paper is of independent interest. It comprises…
Let $V$ be an operator space and $\iso(V)$ be the group of all completely isometric bijective linear mappings on $V$. Let $G$ act on $V$ via a strongly continuous group homomorphism $\alpha:G \to \iso (V)$. We define the full (and reduced)…
In this paper, first we study surjective isometries (not necessarily linear) between completely regular subspaces $A$ and $B$ of $C_0(X,E)$ and $C_0(Y,F)$ where $X$ and $Y$ are locally compact Hausdorff spaces and $E$ and $F$ are normed…
We prove that for every closed locally convex subspace $E$ of $L_0$ and for any continuous linear operator $T$ from $L_0$ to $L_0/E$ there is a continuous linear operator $S$ from $L_0$ to $L_0$ such that $T = QS$ where $Q$ is the quotient…
We consider a generalization of Hausdorff operators on Lebesgue spaces and under natural conditions prove that such an operator is not a Riesz operator provided it is non-zero. In particular, it cannot be represented as a sum of a…
In the paper, we revisit several approaches to the concept of uniform completion $X^{\mathrm{ru}}$ of a vector lattice $X$. We show that many of these approaches yield the same result. In particular, if $X$ is a sublattice of a uniformly…
A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space $\H$ are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can…
The purpose of this paper is to give an overview of the operator structure of frames, where the operator belongs to certain classes of linear operators and the element belongs to $H$. We discuss the size of the set of such elements. Also,…