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

[EN] 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.Both authors were supported by the Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigacion (Spain) and FEDER, the first author under project PGC2018-095366-B-100 and the second under project MTM2016-77054-C2-1-P.Calabuig, JM.; Sánchez Pérez, EA. (2021). Absolutely (q, 1)-summing operators acting in C(K)-spaces and the weighted Orlicz property for Banach spaces. Positivity. 25(3):1199-1214. https://doi.org/10.1007/s11117-021-00811-y1199121425