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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09377-5
PII: S 0002-9939(08)09377-5
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.