Related papers: Isometries between completely regular vector-value…

In order to generalize the results of Mazur-Ulam and Vogt, we shall prove that any map T which preserves equality of distance with T(0)=0 between two F-spaces without surjective condition is linear. Then, as a special case linear isometries…

A space $X$ is called $CCS$-normal space if there exist a normal space $Y$ and a bijection $f: X\mapsto Y$ such that $f\lvert_C:C\mapsto f(C)$ is homeomorphism for any cellular-compact subset $C$ of $X$. We discuss about the relations…

This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…

We characterize the surjective isometries, with respect to the Hausdorff distance, of the class of bodies given by intersections of Euclidean unit balls. We show that any such isometry is given by the composition of a rigid motion with…

Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space ${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal B}({\mathcal H})$ by…

We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of…

This paper has two goals: to present some new results that are necessary for further study and applications of quasi-linear functionals, and, by combining known and new results, to serve as a convenient single source for anyone interested…

In this paper, we consider the linear direct sum of a real normed linear space with an order unit space and with a base normed space to obtain respectively a new order unit space and a new base normed space. As a consequence, we find that…

Necessary and sufficient conditions are already known in the Hardy spaces of both the disc and the half plane for a composition operator to be an isometry, by Nordgren in the disc and by Chalendar and Partington in the half plane. All the…

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…

For non-Archimedean spaces $ X $ and $ Y, $ let $ \mathcal{M}_{\flat } (X), \mathfrak{M}(V \rightarrow W) $ and $ \mathfrak{D}_{\flat }(X, Y) $ be the ballean of $ X $ (the family of the balls in $ X $), the space of mappings from $ X $ to…

Let $\mathcal{H}$ be a complex, separable Hilbert space and $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on…

We consider the Segal-Bargmann transform for a noncompact symmetric space of the complex type. We establish isometry and surjectivity theorems for the transform, in a form as parallel as possible to the results in the compact case. The…

Let $X$ and $Y$ be locally compact Hausdorff spaces. We denote by $C_0^+(X)$ the positive cone of all real-valued continuous functions on $X$ vanishing at infinity. In this paper, we consider a bijection $T\colon C_0^+(X) \to C_0^+(Y)$…

We describe absolutely ordered $p$-normed spaces, for $1 \le p \le \infty$ which presents a model for "non-commutative" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of…

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…

In this paper we prove that an isometry between orbit spaces of two proper isometric actions is smooth if it preserves the codimension of the orbits or if the orbit spaces have no boundary. In other words, we generalize Myers-Steenrod's…

Let $S$ be a non-empty, closed subspace of a locally compact group $G$ that is a subsemigroup of $G$. Suppose that $X, Y$, and $Z$ are Banach lattices that are vector sublattices of the order dual $\mathrm{C}_{\mathrm{c}}(S,\mathbb R)^\sim$…

Let $X$ be a compact Hausdorff space, let $E$ be a Banach space, and let $C(X,E)$ stand for the Banach space of $E$-valued continuous functions on $X$ under the uniform norm. In this paper we characterize Integral operators (in the sense of…

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…