Villanueva Díez, 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
Official URL: http://www.staff.amu.edu.pl/ fa/
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)×• • •× C(Kd) (Ki – Hausdorff compact spaces) to C(K1)__×• • •×C(Kd)__ that are separately weak_-continuous is established. As a corollary, integral representations with respect to polymeasures for multilinear mappings on C(K1)×• • •×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.
|Uncontrolled Keywords:||Multilinear mapping; Dual space; compact Hausdorff space; Polymeasure; Multilinear operators|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
|Deposited On:||07 Mar 2011 12:22|
|Last Modified:||06 Mar 2013 16:27|
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