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Upper bound for isometric embeddings
Authors:Yu. I. Lyubich
Affiliation:Department of Mathematics, Technion, 32000, Haifa, Israel
Abstract:The isometric embeddings $ ell_{2;mathbb{K}}^m rightarrowell_{p;mathbb{K}}^n$ ($ mgeq 2$, $ pin 2mathbb{N}$) over a field $ mathbb{K}inlbrace 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}neqmathbb{H}$) the bound was obtained by Delbaen, Jarchow and Pełczyński (1998) in a different way.

Keywords:Isometric embeddings   quaternion spaces.
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