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Villanueva, Ignacio
(2000)
*Completely continuous multilinear operators on C(K) spaces.*
Proceedings of the American Mathematical Society, 128
.
pp. 793-801.
ISSN 1088-6826

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Official URL: http://www.ams.org/publications/journals/journalsframework/proc

## Abstract

Given a k-linear operator T from a product of C(K) spaces into a Banach space X, our main result proves the equivalence between T being completely continuous, T having an X-valued separately omega* - omega* continuous extension to the product of the biduals and T having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to T being weakly compact, and that, for k > 1, T being weakly compact implies the conditions above but the converse fails.

Item Type: | Article |
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Uncontrolled Keywords: | C(K) spaces, Completely continuous, Multilinear operators, Aron-Berner extension |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 11422 |

Deposited On: | 28 Oct 2010 10:23 |

Last Modified: | 06 Feb 2014 09:03 |

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