Absolutely (q, 1)-summing operators acting in C(K)-spaces and the weighted Orlicz property for Banach spaces

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