Open Access
december 2018 A note on the Vestfrid theorem
Yu Zhou, Zihou Zhang, Chunyan Liu
Bull. Belg. Math. Soc. Simon Stevin 25(4): 541-544 (december 2018). DOI: 10.36045/bbms/1546570908

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 $u\in X$.

Citation

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Yu Zhou. Zihou Zhang. Chunyan Liu. "A note on the Vestfrid theorem." Bull. Belg. Math. Soc. Simon Stevin 25 (4) 541 - 544, december 2018. https://doi.org/10.36045/bbms/1546570908

Information

Published: december 2018
First available in Project Euclid: 4 January 2019

zbMATH: 07038167
MathSciNet: MR3896270
Digital Object Identifier: 10.36045/bbms/1546570908

Subjects:
Primary: 46B04
Secondary: 41A65 , 46B20

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

Rights: Copyright © 2018 The Belgian Mathematical Society

Vol.25 • No. 4 • december 2018
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