A Remark on Two Duality Relations

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 , denoting by N(K, T) the minimal number of translates of T needed to cover K, one has: , where 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 functionals.