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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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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X02003621

## Abstract

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 |

Deposited On: | 01 Dec 2010 10:50 |

Last Modified: | 06 Feb 2014 09:08 |

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