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Euclidean Sections of Direct Sums of Normed Spaces |
Canad. Math. Bull. 46(2003), 242-251
Published:2003-06-01
Printed: Jun 2003
Printed: Jun 2003
- A. E. Litvak
- V. D. Milman
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 |
| MSC Classifications: |
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] |