This is an announcement for the paper "A remark on two duality relations" by Emanuel Milman.

Abstract: We remark that an easy combination of two known results yields a positive answer, up to log(n) terms, to a duality conjecture that goes back to Pietsch. In particular, we show that for any two symmetric convex bodies K,T in R^n, denoting by N(K,T) the minimal number of translates of T needed to cover K, one has: N(K,T) <= N(T*,(C log(n))^{-1} K*)^{C log(n) loglog(n)}, where K*,T* are the polar bodies to K,T, respectively, and C > 1 is a universal constant. As a corollary, we observe a new duality result (up to log(n) terms) for Talagrand's \gamma_p functionals.

Archive classification: Functional Analysis; Metric Geometry

Remarks: 13 pages

The source file(s), Duality-Of-Entropy.bbl: 4703 bytes, Duality-Of-Entropy.tex: 31314 bytes, is(are) stored in gzipped form as 0603461.tar.gz with size 12kb. The corresponding postcript file has gzipped size 60kb.

Submitted from: emanuel.milman@weizmann.ac.il

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