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A proportional Dvoretzky-Rogers
factorization result

Author: A. A. Giannopoulos
Journal: Proc. Amer. Math. Soc. 124 (1996), 233-241
MSC (1991): Primary 46B07
MathSciNet review: 1301496
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Abstract: If $X$ is an $n$-dimensional normed space and $\varepsilon\in(0,1)$, there exists $m\geq(1-\varepsilon)n$, such that the formal identity $i_{2,\infty}\colon l^m_2\to l^m_\infty$ can be written as $i_{2,\infty}=\alpha\circ\beta,\beta\colon l^m_2\to X,\alpha\colon X\to l^m_\infty$, with $\|\alpha\|\cdot\|\beta\|\leq c/\varepsilon$. This is proved as a consequence of a Sauer-Shelah type theorem for ellipsoids.

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Additional Information

A. A. Giannopoulos
Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
Address at time of publication: Department of Mathematics, University of Crete, Iraklion, Crete, Greece

Received by editor(s): February 21, 1994
Received by editor(s) in revised form: August 15, 1994
Communicated by: Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society