Absolutely \((q, 1)\)-summing operators acting in \(C(K)\)-spaces and the weighted Orlicz property for Banach spaces
The authors present the main result which is a characterization of the class of homogeneous weights for which the coincidence of weak weighted summable and norm summable sequences in a Banach space implies that it is finite dimensional. In order to do this, the notion of weighted \((q,\phi )\)-Orlicz property for a Banach space is introduced. Then Pisier's Theorem can be proved using the same standard separation argument that proves Pietsch's Theorem and Maurey-Rosenthal's Theorem.
scientific article; zbMATH DE number 7382093
scientific article