ISOMETRIC EMBEDDINGS OF COMPACT SPACES INTO BANACH SPACES

By Y. Dutrieux, G. Lancien. 2008

49 citations recorded by the source corpus.

We show the existence of a compact metric space $K$ such that whenever $K$ embeds isometrically into a Banach space $Y$, then any separable Banach space is linearly isometric to a subspace of $Y$. We also address the following related question: if a Banach space $Y$ contains an isometric copy of the unit ball or of some special compact subset of a separable Banach space $X$, does it necessarily contain a subspace isometric to $X$? We answer positively this question when $X$ is a polyhedral finite-dimensional space, $c_0$ or $\ell_1$.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8a401a0dfd351fb033cc38256cde18922b1d403b

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In Applied Mathematics

1. Wen Zhang
2. Y. Dong
3. Lixin Cheng

In Mathematical Physics

1. Wen Zhang
2. Y. Dong
3. Lixin Cheng

Citations in the corpus

• On stability of nonlinear non-surjective ε-isometries of Banach spaces (2013, methodology): “The following result was first noticed by Dutrieux and Lancien [5], and it is equivalent to Figiel’s theorem.”