A famous result of S. Kwapień asserts that a linear operator from Banach space to Hilbert is absolutely 1-summing whenever its adjoint q-summing for some 1 ≤ q < ∞; this was recently extended Lipschitz operators by Chen and Zheng. In the present paper we show Kwapień’s Chen-Zheng’s theorems hold in very relaxed nonlinear environment, under weaker hypotheses. Even when restricted original case, ...

Let \(X\), \(Y\) and \(Z\) be Banach spaces let \(U\) a subspace of \(\mathcal{L}(X^*,Y)\), the space all operators from \(X^*\) to \(Y\). An operator \(S\colon U \to Z\) is said \((\ell^s_p,\ell_p)\)-summing (where \(1\leq p <\infty\)) if there constant \(K\geq 0\) such that \(\left( \sum_{i=1}^n \|S(T_i)\|_Z^p \right)^{1/p}\le K\sup_{x^* \in B_{X^*}} \left(\sum_{i=1}^n \|T_i(x^*)\|_Y^p\right...