0$, into various type of Banach or quasi-Banach spaces. In particular, for $0 <r < p<2$ with $r \le 1$, we construct a family of operators

This is an announcement for the paper "Sparsity and non-Euclidean embeddings" by Omer Friedland and Olivier Guedon. Abstract: We present a relation between sparsity and non-Euclidean isomorphic embeddings. We introduce a general restricted isomorphism property and show how it enables to construct embeddings of $\ell_p^n$, $p that embed $\ell_p^n$ into $\ell_r^{(1+\eta)n}$, with optimal polynomial bounds in $\eta >0$. Archive classification: math.FA Submitted from: omerfrie@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.0992 or http://arXiv.org/abs/1107.0992