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Multilinear operators on spaces of continuous functions

Villanueva, Ignacio and Bombal Gordón, Fernando (1998) Multilinear operators on spaces of continuous functions. Functiones et Approximatio. Commentarii Mathematici, 26 . pp. 117-126. ISSN 0208-6573

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Abstract

Let E1, . . . ,Ed be Banach spaces such that all linear operators from Ei into E_j (i 6= j) are weakly compact. The authors show that every continuous d-linear operator T on E1 × • • • × Ed to a Banach space F possesses a unique bounded multilinear extension T__ : E__ 1 × • • • × E__ d ! F__ that is !_ − !_-separately continuous and kT__k = kTk. In particular, existence of unique continuous multilinear extensions from C(K1)ו • •× C(Kd) (Ki – Hausdorff compact spaces) to C(K1)__ו • •×C(Kd)__ that are separately weak_-continuous is established. As a corollary, integral representations with respect to polymeasures for multilinear mappings on C(K1)ו • •×C(Kd) into a Banach space are found. The results generalize a theorem due to Pelczynsky about multilinear extensions from C(K1) × • • • × C(Kd) to the Cartesian product of the spaces of bounded Baire functions on Ki.


Item Type:Article
Uncontrolled Keywords:Multilinear mapping; Dual space; compact Hausdorff space; Polymeasure; Multilinear operators
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:12357
Deposited On:07 Mar 2011 11:22
Last Modified:06 Feb 2014 09:23

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