  Given an infinite set \Lambda of characters on a compact abelian group we
show that \Lambda is a \Lambda(p)-set for all p>2 if and only if the limit
order of the ideal of all \Lambda-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 \Lambda is 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.
