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
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2486
or
http://arXiv.org/abs/0801.2486
or by email in unzipped form by transmitting an empty message with subject line
uget 0801.2486
or in gzipped form by using subject line
get 0801.2486
to: math@arXiv.org.