A sharp dual L_p John ellipsoid problem for p ≤ -n - 1

摘要

When p > 0, the dual L_p John ellipsoids provide a unified treatment for the L?wner ellipsoid and the Legendre ellipsoid associated with a convex body.When p < 0, very little relevance to known ellipsoids has been found for the dual L_p John ellipsoid so far. In this paper we investigate a sharp dual L_p John ellipsoid problem associated with origin-symmetric convex bodies when p ≤ -n - 1. The solution unifies the classic John ellipsoid and the classic Petty ellipsoid.