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oai:docta.ucm.es:20.500.14352/569442024-07-12T15:59:15Zcom_20.500.14352_14col_20.500.14352_15

Integral mappings between Banach spaces Villanueva Díez, Ignacio 517 519.6 Integral operators Multilinear operators Spaces of continuous functions Injective tensor product Análisis matemático 1202 Análisis y Análisis Funcional We 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. DGICYT Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:46:28Z 2023-06-20T16:46:28Z 2003 journal article https://hdl.handle.net/20.500.14352/56944 0022-247X 10.1016/S0022-247X(02)00362-1 eng PB97-0240 Villanueva 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. open access application/pdf Elsevier