This is an announcement for the paper "Upper bound for isometric embeddings \ell_2^m\to\ell_p^n" by Yuri I. Lyubich. Abstract: The isometric embeddings $\ell_{2;K}^m\to\ell_{p;K}^n$ ($m\geq 2$, $p\in 2\N$) over a field $K\in{R, C, H}$ are considered, and an upper bound for the minimal $n$ is proved. In the commutative case ($K\neq H$) the bound was obtained by Delbaen, Jarchow and Pe{\l}czy{\'n}ski (1998) in a different way. Archive classification: math.FA Mathematics Subject Classification: 46B04 Remarks: 5 pages The source file(s), upbound.bbl: 1810 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0712.0214 or http://arXiv.org/abs/0712.0214 or by email in unzipped form by transmitting an empty message with subject line uget 0712.0214 or in gzipped form by using subject line get 0712.0214 to: math@arXiv.org.