Complutense University Library

Multilinear operators on spaces of continuous functions

Impacto




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

[img]
Preview
PDF
184kB

Official URL: http://www.staff.amu.edu.pl/ fa/




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

Repository Staff Only: item control page