Interpolation estimates for entropy numbers with applications to non-convex bodies

Abstract

We complement classical results on the interpolation of entropy numbers as well as certain $s$-numbers and present an application to a class of non-convex bodies which are generalizations of $p$-convex bodies. In particular we apply the estimates of entropy numbers of operators on Calderón–Lozanovskii spaces to approximation of the volume of $\phi$-absolute convex hull of $n$ points in ${\mathbb{R}}^k$ generated by a class of concave functions.