Duality of metric entropy in Euclidean space

Shiri Artstein, Vitali D. Milman, Stanislaw J. Szarek

Research output: Contribution to journalArticlepeer-review

Abstract

Let K be a convex body in a Euclidean space, K○ its polar body and D the Euclidean unit ball. We prove that the covering numbers N (K, t D) and N (D, t K○) are comparable in the appropriate sense, uniformly over symmetric convex bodies K, over t > 0 and over the dimension of the space. In particular this verifies the duality conjecture for entropy numbers of linear operators, posed by Pietsch in 1972, in the central case when either the domain or the range of the operator is a Hilbert space.

Original languageEnglish
Pages (from-to)711-714
Number of pages4
JournalComptes Rendus Mathematique
Volume337
Issue number11
DOIs
StatePublished - 1 Dec 2003

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