We provide a new separation-based proof of the domination theorem for (q, 1)-summing operators. This result gives the celebrated factorization theorem of Pisier for (q, 1)-summing operators acting in C(K)-spaces. As far as we know, none of the known versions of the proof uses the separation argument presented here, which is essentially the same that proves Pietsch Domination Theorem for p-summing operators. Based on this proof, we propose an equivalent formulation of the main summability properties for operators, which allows to consider a broad class of summability properties in Banach spaces. As a consequence, we are able to show new versions of the Dvoretzky–Rogers Theorem involving other notions of summability, and analyze some weighted extensions of the q-Orlicz property.

我们为（q，1）加和运算符提供了一个新的基于分离的控制定理的证明。这个结果给出了在（C，K）空间中作用的（q，1）个求和算子的Pisier著名的因式分解定理。据我们所知，证明的已知版本均未使用此处提出的分离参数，该参数与证明p的Pietsch支配定理基本相同求和运算符。基于此证明，我们为算子提出了主要可加性的等价表示形式，它允许考虑Banach空间中一类广泛的可加性。结果，我们能够展示涉及其他可加性概念的Dvoretzky-Rogers定理的新版本，并分析q -Orlicz属性的一些加权扩展。