相关论文: On large $\ell_1$-sums of Lipschitz-free spaces an…

Let (X, d) be a bounded metric space with a base point 0 X , (Y, $\bullet$) be a Banach space and Lip $\alpha$ 0 (X, Y) be the space of all $\alpha$-H{\"o}lderfunctions that vanish at 0 X , equipped with its natural norm (0 < $\alpha$ $\le$…

The goal of this paper is to study geometric and extremal properties of the convex body $B_{\mathcal F(M)}$, which is the unit ball of the Lipschitz-free Banach space associated with a finite metric space $M$. We investigate $\ell_1$ and…

If $X$ is a topological space and $\kappa$ is a cardinal then $\mathsf{BA}_\kappa (X)$ is the statement that for each pair $A, B \subseteq X$ of $\kappa$-dense subsets there is an autohomeomorphism $h:X \to X$ mapping $A$ to $B$. In…

We prove that: I. If $L$ is a $T_1$ space, $|L|>1$ and $d(L) \leq \kappa \geq \omega$, then there is a submaximal dense subspace $X$ of $L^{2^\kappa}$ such that $|X|=\Delta(X)=\kappa$; II. If $\frak{c}\leq\kappa=\kappa^\omega<\lambda$ and…

In the short note we prove that for every $0<p<1$, there exists an infinite dimensional closed linear subspace of $\mathcal{L}\left( \ell_{p};\ell_{p}\right) $ every nonzero element of which is non $(r,s)$-absolutely summing operator for…

In the present note we give a construction (based on a retractional argument) of a Schauder basis for the Lipschitz free space $\mathcal{F}(N)$, over a net $N$ in any separable infinite dimensional $\mathcal{L}_\infty$-space $X$. In…

Let $T$ be a topological space admitting a compatible proper metric, that is, a locally compact, separable and metrisable space. Let $\mathcal{M}^T$ be the non-empty set of all proper metrics $d$ on $T$ compatible with its topology, and…

We study several properties and applications of the ultrapower $M_{\mathcal U}$ of a metric space $M$. We prove that the Lipschitz-free space $\mathcal F(M_{\mathcal U})$ is finitely representable in $\mathcal F(M)$. We also characterize…

We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces $L_X^p$, where $X$ is a Banach space and $1\le p<\infty$, and extend the result to vector-valued Banach function spaces…

The classical theorems of Banach and Stone, Gelfand and Kolmogorov, and Kaplansky show that a compact Hausdorff space $X$ is uniquely determined by the linear isometric structure, the algebraic structure, and the lattice structure,…

For a domain $\Omega$ in a finite-dimensional space $E$, we consider the space $M=(\Omega,d)$ where $d$ is the intrinsic distance in $\Omega$. We obtain an isometric representation of the space $\mathrm{Lip}_{0}(M)$ as a subspace of…

In the present paper we introduce and study the Lipschitz retractional structure of metric spaces. This topic was motivated by the analogous projectional structure of Banach spaces, a topic that has been thoroughly investigated. The more…

We find a new finite algorithm for evaluation of Lipschitz-free $p$-space norm in finite-dimensional Lipschitz-free $p$-spaces. We use this algorithm to deal with the problem of whether given $p$-metric spaces $N\subset M$, the canonical…

In this short note we prove the result stated in the title; that is, for every $p>0$ there exists an infinite dimensional closed linear subspace of $L_{p}[0,1]$ every nonzero element of which does not belong to $\bigcup\limits_{q>p}…

All spaces are assumed to be Tychonoff. Given a realcompact space $X$, we denote by $\mathsf{Exp}(X)$ the smallest infinite cardinal $\kappa$ such that $X$ is homeomorphic to a closed subspace of $\mathbb{R}^\kappa$. Our main result shows…

We show that on separable Banach spaces admitting a separating polynomial, any uniformly continuous, bounded, real-valued function can be uniformly approximated by Lipschitz, analytic maps on bounded sets.

Following results of Bourgain and Gorelik we show that the spaces $\ell_p$, $1<p<\infty$, as well as some related spaces have the following uniqueness property: If $X$ is a Banach space uniformly homeomorphic to one of these spaces then it…

We prove that if $M$ is an infinite complete metric space then the set of strongly norm-attaining Lipschitz functions $\SA(M)$ contains a linear subspace isomorphic to $c_0$. This solves an open question posed by V. Kadets and O. Rold\'an.

A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Frechet differentiability. We show that the answer is positive for some…

Cembranos and Freniche proved that for every two infinite compact Hausdorff spaces $X$ and $Y$ the Banach space $C(X\times Y)$ of continuous real-valued functions on $X\times Y$ endowed with the supremum norm contains a complemented copy of…