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Integral mappings between Banach spaces

Villanueva, Ignacio (2003) Integral mappings between Banach spaces. Journal of Mathematical Analysis and Applications, 279 (1). pp. 56-70. ISSN 0022-247X


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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.

Item Type:Article
Uncontrolled Keywords:Integral operators, Multilinear operators, Spaces of continuous functions, Injective tensor product
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:11653

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