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


Author: Yu. I. Lyubich
Journal: Proc. Amer. Math. Soc. 136 (2008), 3953-3956
MSC (2000): Primary 46B04
DOI: https://doi.org/10.1090/S0002-9939-08-09377-5
Published electronically: June 2, 2008
MathSciNet review: 2425735
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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.


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Additional Information

Yu. I. Lyubich
Affiliation: Department of Mathematics, Technion, 32000, Haifa, Israel
Email: lyubich@tx.technion.ac.il

Keywords: Isometric embeddings, quaternion spaces.
Received by editor(s): August 1, 2007
Received by editor(s) in revised form: October 3, 2007
Published electronically: June 2, 2008
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.