A note on uniformly dominated sets of summing operators (Q1607851)

Summary: Let \(Y\) be a Banach space that has no finite cotype and \(p\) a real number satisfying \(1 \leq p < \infty\). We prove that a set \(\mathcal{M} \subset \Pi_p(X,Y)\) is uniformly dominated if and only if there exists a constant \(C > 0\) such that, for every finite set \(\{(x_i,T_i):i = 1, \dots,n\} \subset X \times \mathcal{M}\), there is an operator \(T \in \Pi_p(X,Y)\) satisfying \(\pi_p(T) \leq C\) and \(\|T_ix_i\|\leq \|Tx_i\|\) for \(i =1,\dots,n\).