Λ(p)-sets and the limit order of operator ideals

Abstract

Given an infinite set Λof characters on a compact abelian group we show that Λis a Λ(p)-set for all p>2 if and only if the limit order of the ideal of all Λ-summing operators coincides with that of the ideal of all Gaussian-summing operators. This is a natural counterpart to a recent result of Baur which says that Λis a Sidon set if and only if even the two operator ideals from above coincide. Furthermore, our techniques, which are mainly based on complex interpolation, lead us to exact asymptotic estimates of the Gaussian-summing norm of identities between finite-dimensional Schatten classes.