Villanueva Díez, Ignacio2023-06-202023-06-2020001088-682610.1090/S0002-9939-99https://hdl.handle.net/20.500.14352/56921Given a k-linear operator T from a product of C(K) spaces into a Banach space X, our main result proves the equivalence between T being completely continuous, T having an X-valued separately omega* - omega* continuous extension to the product of the biduals and T having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to T being weakly compact, and that, for k > 1, T being weakly compact implies the conditions above but the converse fails.engjournal articlehttps//doi.org/10.1090/S0002-9939-99http://www.ams.org/publications/journals/journalsframework/procopen access517.98C(K) spacesCompletely continuousMultilinear operatorsAron-Berner extensionAnálisis funcional y teoría de operadores