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A proportional Dvoretzky-Rogers factorization result
Authors:A. A. Giannopoulos
Affiliation:Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
Abstract:If $X$ is an $n$-dimensional normed space and $varepsilonin(0,1)$, there exists $mgeq(1-varepsilon)n$, such that the formal identity $i_{2,infty}colon l^m_2to l^m_infty$ can be written as $i_{2,infty}=alphacircbeta,betacolon l^m_2to X,alphacolon Xto l^m_infty$, 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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