$(r,p)$-absolutely summing operators on the space $C(T,X)$ and applications

Abstract

We give necessary and sufficient conditions for an operator on the space $C\left(T,X\right)$ to be $\left(r,p\right)$-absolutely summing. Also we prove that the injective tensor product of an integral operator and an $\left(r,p\right)$-absolutely summing operator is an $\left(r,p\right)$-absolutely summing operator.