Villanueva Díez, Ignacio2023-06-202023-06-202003Villanueva Díez, I. «Integral Mappings between Banach Spaces». Journal of Mathematical Analysis and Applications, vol. 279, n.o 1, marzo de 2003, pp. 56-70. DOI.org (Crossref), https://doi.org/10.1016/S0022-247X(02)00362-1.0022-247X10.1016/S0022-247X(02)00362-1https://hdl.handle.net/20.500.14352/56944We consider the classes of “Grothendieck-integral” (G-integral)and “Pietsch-integral” (P-integral) linear and multilinear operators (see definitions below), and we prove that a multilinear operator between Banach spaces is G-integral (resp. P-integral) if and only if its linearization is G-integral (resp. P-integral) on the injective tensor product of the spaces, together with some related results concerning certain canonically associated linear operators. As an application we give a new proof of a result on the Radon-Nikodym property of the dual of the injective tensor product of Banach spaces. Moreover, we give a simple proof of a characterization of the G-integral operators on C(K,X) spaces and we also give a partial characterization of P-integral operators on C(K,X) spaces.engjournal articlehttps//doi.org/10.1016/S0022-247X(02)00362-1http://www.sciencedirect.com/science/article/pii/S0022247X02003621open access517519.6Integral operatorsMultilinear operatorsSpaces of continuous functionsInjective tensor productAnálisis matemático1202 Análisis y Análisis Funcional