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Euclidean Sections of Direct Sums of Normed Spaces

Published online by Cambridge University Press:  20 November 2018

A. E. Litvak  and
V. D. Milman
A. E. Litvak
Affiliation:
Department of Mathematics, Technion, Haifa, Israel, e-mail: alex@math.technion.ac.il Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, e-mail: alexandr@math.ualberta.ca
V. D. Milman
Affiliation:
Department of Mathematics, Tel Aviv University, Tel Aviv, Israel, e-mail: milman@post.tau.ac.il
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Abstract

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We study the dimension of “random” Euclidean sections of direct sums of normed spaces. We compare the obtained results with results from $[\text{LMS}]$, 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 1.4 and explanation after). We also add some relative information on “phase transition”.

Keywords

46B0746B0946B2052A21Dvoretzky theorem“random” Euclidean sectionphase transition in asymptotic convexity
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 2 , 01 June 2003 , pp. 242 - 251
Copyright
Copyright © Canadian Mathematical Society 2003

References

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