Nuclear multilinear operators with respect to a Banach ideal of multilinear functionals

Abstract

We introduce the concept of p-nuclear multilinear operator (1≤p≤∞) with respect to a Banach ideal of multilinear functionals and prove some Pietsch type composition results for this class. As an application we prove that each compact operator from C(Ω) into a cotype 2 space is 2-nuclear. By an example we show that the corresponding multilinear result is not true in general.