## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

### A note on the Vestfrid theorem

Yu Zhou, Zihou Zhang, and Chunyan Liu

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1546570908

**Mathematical Reviews number (MathSciNet)**

MR3896270

**Subjects**

Primary: 46B04: Isometric theory of Banach spaces

Secondary: 46B20: Geometry and structure of normed linear spaces 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

**Keywords**

$\varepsilon$-isometric embedding Hyers-Ulam stability Banach spaces of continuous functions

#### Citation

Zhou, Yu; Zhang, Zihou; Liu, Chunyan. A note on the Vestfrid theorem. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 4, 541--544. https://projecteuclid.org/euclid.bbms/1546570908