Related papers: On linear operators extending [pseudo]metrics

In this paper, we establish the existence of a bounded, linear extension operator $T: L^{2,p}(E) \to L^{2,p}(\mathbb{R}^2)$ when $1<p<2$ and $E$ is a finite subset of $\mathbb{R}^2$ contained in a line.

We investigate the problem of existence of a bounded extension to $C(K)$ of a bounded $c_0(I)$-valued operator $T$ defined on the subalgebra of $C(K)$ induced by a continuous increasing surjection $\phi:K\to L$, where $K$ and $L$ are…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

One proves that any everywhere defined constructive mapping from a complete metric space into a complete metric space which preserves the property of precompacity of subsets is locally uniformly continuous. This fact can be viewed as…

We consider a matrix semigroup $T: [0,\infty) \to \mathbb{R}^{d \times d}$ without assuming any measurability properties and show that, if $T$ is bounded close to $0$ and $T(t) \ge 0$ entrywise for all $t$, then $T$ is continuous. This…

We characterize the restrictions of first order Sobolev functions to regular subsets of a homogeneous metric space and prove the existence of the corresponding linear extension operator.

We introduce sufficient as well as necessary conditions for a compact set $K$ such that there is a continuous linear extension operator from the space of restrictions $C^\infty(K)=\lbrace F|_K: F\in C^\infty(\mathbb R)\rbrace$ to…

We first prove a version of Tietze-Urysohn's theorem for proper functions taking values in non-negative real numbers defined on $\sigma$-compact locally compact Hausdorff spaces. As its application, we prove an extension theorem of proper…

The paper deals with continuous homomorphisms $S \ni s \mapsto T_s \in L(E)$ of amenable semigroups $S$ into the algebra $L(E)$ of all bounded linear operators on a Banach space $E$. For a closed linear subspace $F$ of $E$, sufficient…

Let $E$ be a real Banach space. For $x,y \in E,$ we follow R.James in saying that $x$ is orthogonal to $y$ if $\|x+\alpha y\|\geq \|x\|$ for every $\alpha \in R$. We prove that every operator from $E$ into itself preserving orthogonality is…

A linear operator $T$ between two lattice-normed locally solid Riesz spaces is said to be $p_\tau$-continuous if, for any $p_\tau$-null net $(x_\alpha)$, the net $(Tx_\alpha)$ is $p_\tau$-null, and $T$ is also said to be $p_\tau$-bounded…

Over a closed manifold, we consider the sectorial projection of an elliptic pseudo-differential operator A of positive order with two rays of minimal growth. We show that it depends continuously on A when the space of pseudo-differential…

In this note we prove a Birkhoff type transitivity theorem for continuous maps acting on non-separable completely metrizable spaces and we give some applications for dynamics of bounded linear operators acting on complex Fr\'{e}chet spaces.…

If $\pi:(X,T)\to(Z,S)$ is a topological factor map between uniquely ergodic topological dynamical systems, then $(X,T)$ is called an isomorphic extension of $(Z,S)$ if $\pi$ is also a measure-theoretic isomorphism. We consider the case when…

Our main technical tool is a principally new property of compact narrow operators which works for a domain space without an absolutely continuous norm. It is proved that for every K\"{o}the $F$-space $X$ and for every locally convex…

We characterize all linear operators on finite or infinite-dimensional spaces of univariate real polynomials preserving the sets of elliptic, positive, and non-negative polynomials, respectively. This is done by means of Fischer-Fock…

We study homeomorphisms of compact metric spaces whose restriction to the nonwandering set has the pseudo-orbit tracing property. We prove that if there are positively expansive measures, then the topological entropy is positive. Some short…

For separable metrizable spaces $X,Y$ and a metrizable topological group $Z$ by $S(X\times Y,Z)$ we denote the space of all separately continuous functions $f:X\times Y\to Z$ endowed with the topology of layer-wise uniform convergence,…

We will remark an extension of a linear functional on subalgebra of algebra of continuous functions on subset of $\mathbb{R}^n$ which preserves positivity.

We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree $p$ with $k$ continuous derivatives. The construction is based on polynomial extension from neighboring elements…