## Bulletin of the Belgian Mathematical Society - Simon Stevin

### A note on the Vestfrid theorem

#### Abstract

Let $X$ be a real Banach space, $T$ be a compact metrizable space, $C(T)$ be the real-valued continuous functions space, and $f:X\rightarrow C(T)$ be a standard $\varepsilon$-isometric embedding. Then for any $\lambda>6$ there is an isometric embedding $h: X\rightarrow C(T)$ such that $\|f(u)-h(u)\|\leq\lambda\varepsilon$ for all $u\in X$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 4 (2018), 541-544.

Dates
First available in Project Euclid: 4 January 2019