A Remark on Two Duality Relations
نویسنده
چکیده
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, 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))K) log(n) log , 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 γp functionals.
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