Quasi‐isometric embeddings of C0(K,X)$C_{0}(K, X)$ spaces which induce isometries whenever X$X$ is a Hilbert space

Elói Medina Galego

Mathematische Nachrichten, 2025, vol. 298, issue 9, 2975-2985

Abstract: Suppose that K$K$ and S$S$ are locally compact Hausdorff spaces and X$X$ is a Hilbert space. It is proven that if there exist real numbers M≥1$M \ge 1$, L≥0$L \ge 0$ and a map T$T$ from C0(K,X)$C_{0}(K,X)$ to C0(S,X)$C_{0}(S,X)$ satisfying 1M∥f−g∥−L≤∥T(f)−T(g)∥≤M∥f−g∥+L,$$\begin{equation*} \frac{1}{M}\Vert f-g\Vert -L\le \Vert T(f)-T(g)\Vert \le M\Vert f-g\Vert +L,\ \end{equation*}$$for every f$f$ and g$g$ in C0(K,X)${C}_{0}(K,X)$, then there are a locally compact subset S0$S_0$ of S$S$ and a proper continuous function φ$\varphi$ of S0$S_0$ onto K$K$, on the assumption that M2

Date: 2025
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