An extension of a Bourgain-Lindenstrauss-Milman inequality

Omer Friedland, Sasha Sodin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let {norm of matrix} ṡ {norm of matrix} be a norm on Rn. Averaging {norm of matrix} (ε1 x1, ..., εn xn) {norm of matrix} over all the 2n choices of over(ε, →) = (ε1, ..., εn) ∈ {- 1, + 1}n, we obtain an expression | | | x | | | which is an unconditional norm on Rn. Bourgain, Lindenstrauss and Milman [J. Bourgain, J. Lindenstrauss, V.D. Milman, Minkowski sums and symmetrizations, in: Geometric Aspects of Functional Analysis (1986/1987), Lecture Notes in Math., vol. 1317, Springer, Berlin, 1988, pp. 44-66] showed that, for a certain (large) constant η > 1, one may average over ηn (random) choices of over(ε, →) and obtain a norm that is isomorphic to | | | ṡ | | |. We show that this is the case for any η > 1.

Original languageEnglish
Pages (from-to)492-497
Number of pages6
JournalJournal of Functional Analysis
Volume251
Issue number2
DOIs
StatePublished - 15 Oct 2007

Keywords

  • Bourgan-Lindenstrauss-Milman inequality
  • Kahane-Khinchin averages
  • Unconditional

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