Upper bound for isometric embeddings $\ell _2^m\rightarrow \ell _p^n$

Abstract:

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