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The isometric embeddings $\ell_{2;K}^m\to\ell_{p;K}^n$ ($m\geq 2$, $p\in2\N$) over a field $K\in{R, C, H}$ are considered, and an upper bound for theminimal $n$ is proved. In the commutative case ($K\neq H$) the bound wasobtained by Delbaen, Jarchow and Pe{\l}czy{\'n}ski (1998) in a different way.

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