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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Upper bound for isometric embeddings $\ell _2^m\rightarrow \ell _p^n$
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by Yu. I. Lyubich PDF
Proc. Amer. Math. Soc. 136 (2008), 3953-3956 Request permission

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
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3953-3956
  • MSC (2000): Primary 46B04
  • DOI: https://doi.org/10.1090/S0002-9939-08-09377-5
  • MathSciNet review: 2425735