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Euclidean Sections of Direct Sums of Normed Spaces

  Published:2003-06-01
 Printed: Jun 2003
  • A. E. Litvak
  • V. D. Milman
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Abstract

We study the dimension of ``random'' Euclidean sections of direct sums of normed spaces. We compare the obtained results with results from \cite{LMS}, to show that for the direct sums the standard randomness with respect to the Haar measure on Grassmanian coincides with a much ``weaker'' randomness of ``diagonal'' subspaces (Corollary~\ref{sle} and explanation after). We also add some relative information on ``phase transition''.
Keywords: Dvoretzky theorem, ``random'' Euclidean section, phase transition in asymptotic convexity Dvoretzky theorem, ``random'' Euclidean section, phase transition in asymptotic convexity
MSC Classifications: 46B07, 46B09, 46B20, 52A21 show english descriptions Local theory of Banach spaces
Probabilistic methods in Banach space theory [See also 60Bxx]
Geometry and structure of normed linear spaces
Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
46B07 - Local theory of Banach spaces
46B09 - Probabilistic methods in Banach space theory [See also 60Bxx]
46B20 - Geometry and structure of normed linear spaces
52A21 - Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
 

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