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Completely continuous multilinear operators on C(K) spaces

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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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
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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