This is an announcement for the paper "An extension of a Bourgain--Lindenstrauss--Milman inequality" by Omer Friedland and Sasha Sodin.

Abstract: Let || . || be a norm on R^n. Averaging || (\eps_1 x_1, \cdots, \eps_n x_n) || over all the 2^n choices of \eps = (\eps_1, \cdots, \eps_n) in { -1, +1 }^n, we obtain an expression ||| . ||| which is an unconditional norm on R^n. Bourgain, Lindenstrauss and Milman showed that, for a certain (large) constant \eta > 1, one may average over (\eta n) (random) choices of \eps and obtain a norm that is isomorphic to ||| . |||. We show that this is the case for any \eta > 1.

Archive classification: math.FA math.PR

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Submitted from: sodinale@post.tau.ac.il

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