Cotype constants and inequalities between summing and integral norms of finite rank operators

Abstract

We establish inequalities between p-integral and absolutely r-summing norms of finite rank operators acting between Banach spaces in which the notion of cotype is considered. Several applications are given: (a) We get estimates, in this context, for the p-integral norm of the identity operator on n-dimensional Banach spaces and for some Banach-Mazur distance. (b) We obtain a sufficient condition for a kernel of weighted Besov type generates a nuclear operator.