Related papers: Characterizing compact sets in $L^p$-spaces and it…

We construct an appropriate metric on the collection of piecewise $\mathcal C^r$ maps defined on a compact interval. Although this metric space turns out to be not complete, we show that it is indeed a Baire space. As an application, we…

We focus our attention on the de Rham operators' underlying properties which are specified by intrinsic effects of differential geometry structures. And then we apply the procedure of regularization in the context of Lipschitz version of de…

We characterize relatively norm compact sets in the regular $C^*$-algebra of finitely generated Coxeter groups using a geometrically defined positive semigroup acting on the algebra.

A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. Almost all…

A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…

We show that $L^p$-spaces over atomless measure spaces can be characterized in terms of a $p$-concavity type geometric property that is related with the Daugavet property.

We give several characterizations of holomorphic mean Besov-Lipschitz space on the unit ball in $\cn $ and appropriate Besov-Lipschitz space and prove the equivalences between them. Equivalent norms on the mean Besov-Lipschitz space involve…

We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…

We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…

The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book…

The standard arithmetic measures of center, the mean and median, have natural topological counterparts which have been widely used in continuum theory. In the context of metric spaces it is natural to consider the Lipschitz continuous…

We give sufficient conditions for Lipschitz-likeness of a class of polyhedral set-valued mappings in Hilbert spaces based on Relaxed Constant Rank Constraint Qualification (RCRCQ) proposed recently by Minchenko and Stakhovsky. To this aim…

We present an overview of some results about characterization of compactness in which the concept of approximation scheme has had a role. In particular, we present several results that were proved by the second author, jointly with Luther,…

A characterization is presented of barycenters of the Radon probability measures supported on a closed convex subset of a given space. A case of particular interest is studied, where the underlying space is itself the space of finite signed…

We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…

In contrast to the usual Lipschitz seminorms associated to ordinary metrics on compact spaces, we show by examples that Lipschitz seminorms on possibly non-commutative compact spaces are usually not determined by the restriction of the…

In this paper, we establish a comprehensive characterization of the generalized Lipschitz classes through the study of the rate of convergence of a family of semi-discrete sampling operators, of Durrmeyer type, in $L^p$-setting. To achieve…

The "potentials" being considered are analogues of classical Riesz potentials of order 1, and the idea is to look at how they might map L^p spaces into Sobolev spaces in various settings.

Using the notion of modulus of continuity at a point of a mapping between metric spaces, we introduce the notion of extensively bounded mappings generalizing that of Lipschitz mappings. We also introduce a metric on it which becomes a norm…

We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have…