Related papers: Lipschitz-free spaces over ultrametric spaces

We show that the Lipschitz free space of a countable simplicial quasi-tree is isomorphic to $\ell^1$. As a consequence, every finitely generated group with Property (QT) of Bestvina--Bromberg--Fujiwara has a proper uniformly Lipschitz…

We characterize the metric spaces whose free space has the bounded approximation property through a Lipschitz analogue of the local reflexivity principle. We show that there exist compact metric spaces whose free spaces fail the…

This paper is devoted to the proof of uniform H\"older and Lipschitz estimates close to oscillating boundaries, for divergence form elliptic systems with periodically oscillating coefficients. Our main point is that no structure is assumed…

We characterize measure spaces such that the canonical map $L_\infty \to L_1^*$ is surjective. In case of $d$ dimensional Hausdorff measure of a complete separable metric space $X$ we give two equivalent conditions. One is in terms of the…

We show that for every complete metric space $M$ there exists another complete metric space $N$ of the same density character such that the curve-flat quotient of $N$ is isometric to $M$. Moreover, we show that if $M$ is compact and…

Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.

Prompted by a recent question of G. Hjorth as to whether a bounded Urysohn space is indivisible, that is to say has the property that any partition into finitely many pieces has one piece which contains an isometric copy of the space, we…

In this paper, we shall establish Banach-Stone type theorems on spaces of uniformly continuous and lipschitz continuous pseudometrics.

Given a metric space with a Borel probability measure, for each integer $N$ we obtain a probability distribution on $N\times N$ distance matrices by considering the distances between pairs of points in a sample consisting of $N$ points…

We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property ($\mathcal{C}$), Talponen's Countable Separation Property, or being a G\^ateaux…

We demonstrate that the set $L^\infty(X, [-1,1])$ of all measurable functions over a Borel measure space $(X, \mathcal B, \mu )$ with values in the unit interval is typically non-polyhedric when interpreted as a subset of a dual space. Our…

These notes present a basic survey on Transportation cost spaces (aka Lipschitzfree spaces, Wasserstein spaces) and their bi-Lipschitz and linear embeddings into $L_1$ spaces. To make these notes as self-contained as possible, we added the…

We present an isometric version of the complementably universal Banach space $\mathbb{P}$ with a Schauder decomposition. The space $\mathbb{P}$ is isomorphic to Pe{\l}czy\'nski's space with a universal basis as well as to Kadec'…

With the aim of representing subsets of Banach spaces as an infinite series using Lipschitz functions, we study a variant of metric frames which we call Lipschitz p-approximate Schauder frames (Lipschitz p-ASFs). We characterize Lipschitz…

With the aim to better understand the intricate geometry of the class of Lipschitz free $p$-spaces $\mathcal{F}_p(\mathcal{M})$ when $0<p<1$, in this note we study their Banach envelopes and prove that if $0<p<1$ and $ \mathcal{M}$ is a…

For a finitely generated group $G$, we introduce an asymmetric pseudometric on projectivized deformation spaces of $G$-trees, using stretching factors of $G$-equivariant Lipschitz maps, that generalizes the Lipschitz metric on Outer space…

In this paper we consider the class of Lipschitz maps on the unit ball $B_X$ of a Banach space $X$, and the question we deal with is whether for any $\lambda>1$ there exists a $\lambda$-Lipschitz fixed-point free mapping $T\colon B_X\to…

We prove that the spaces $\ell_p$, $1<p<\infty, p\ne 2$, and all infinite-dimensional subspaces of their quotient spaces do not admit equivalent almost transitive renormings. This is a step towards the solution of the Banach-Mazur rotation…

Let $X$ be a Banach space with an unconditional finite-dimensional Schauder decomposition $(E_n)$. We consider the general problem of characterizing conditions under which one can construct an unconditional basis for $X$ by forming an…

We study the geometry of the space of measures of a compact ultrametric space X, endowed with the L^p Wasserstein distance from optimal transportation. We show that the power p of this distance makes this Wasserstein space affinely…