Integral mappings between Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:279

Article

Villanueva, I

关键词: integral operators;    multilinear operators;    spaces of continuous functions;    injective tensor product;   

DOI  :  10.1016/S0022-247X(02)00362-1

来源: Elsevier

【 摘 要 】

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. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

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