Upper bound for isometric embeddings \ell_2^m\to\ell_p^n

Abstract

The isometric embeddings ${\ell }_{2;K}^m\to {\ell }_{p;K}^n$ ($m\ge 2$, $p\in 2\mathbb{N}$) over a field $K\in R,C,H$ are considered, and an upper bound for the minimal $n$ is proved. In the commutative case ($K\ne H$) the bound was obtained by Delbaen, Jarchow and Pełczy{ń}ski (1998) in a different way.

5 pages