  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.
