This is an announcement for the paper "Isometric embeddings of compact spaces into Banach spaces" by Yves Dutrieux Gilles Lancien.

Abstract: 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 $\ell_1$.

Archive classification: math.FA

Mathematics Subject Classification: 46B04; 46B20

Remarks: 8 pages

The source file(s), dutrieux_lancien.tex: 22590 bytes, is(are) stored in gzipped form as 0801.2486.gz with size 8kb. The corresponding postcript file has gzipped size 79kb.

Submitted from: gilles.lancien@univ-fcomte.fr

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