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Upper bound for isometric embeddings

Authors:	Yu I Lyubich

Institution:	Department of Mathematics, Technion, 32000, Haifa, Israel

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 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.

Keywords:	Isometric embeddings quaternion spaces

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