Geometry of spaces between polytopes and related zonotopes

Yehoram Gordon, Alexander Litvak, Carsten Schütt, Elisabeth Werner

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We study geometric parameters associated with the Banach spaces ((double-struck R)n, ∥ · ∥k,q) normed by ∥x∥k,q = (∑1<i≤k [x, ai] *q)1/q, where {ai}i≤N is a given sequence of N points in (double-struck R)n, 1 ≤ k ≤ N, 1 ≤ q ≤ ∞, and {λi*}i≥1 denotes the decreasing rearrangement of a sequence {λi}i≥1 ⊂(double-struck R).

Original languageEnglish (US)
Pages (from-to)733-762
Number of pages30
JournalBulletin des Sciences Mathematiques
Volume126
Issue number9
DOIs
StatePublished - Nov 2002

Bibliographical note

Funding Information:
* Corresponding author. E-mail address: gordon@techunix.technion.ac.il (Y. Gordon). 1 Partially supported by Nato Collaborative Linkage Grant PST.CLG.977406. 2 Partially supported by France–Israel Arc-en-Ciel exchange. 3 Partially supported by the Fund for the Promotion of Research at the Technion. 4 Partially supported by a Lady Davis Fellowship. 5Partially supported by National Science Foundation Grant DMS-0072241 and by Nato Collaborative Linkage Grant PST.CLG.976356.

Keywords

  • Dvoretzky's theorem
  • Polytopes
  • Random variables
  • Volume ratio
  • Zonoids
  • p-summing norm

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