Uniformly summing sets of operators on spaces of continuous functions (Q1777860)

Summary: Let \(X\) and \(Y\) be Banach spaces. A set \({\mathcal M}\) of 1-summing operators from \(X\) into \(Y\) is said to be uniformly summing if the following holds: given a weakly 1-summing sequence \((x_n)\) in \(X\), the series \(\sum_{n}\| Tx_n\|\) is uniformly convergent in \(T\in{\mathcal M}\). We study some general properties and obtain a characterization of these sets when \(\mathcal M\) is a set of operators defined on spaces of continuous functions.