Continuous multilinear operators on C(K) spaces and polymeasures

Autores: Fernando Bombal Gordón
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 22, Nº 2, 2007 (Ejemplar dedicado a: Banach space theory: classical topics and new directions. Cáceres 2006), págs. 127-146
Idioma: inglés
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Resumen
- Every continuous k-linear operator from a product C(K1) × · · · × C(Kk) into a Banach space X (Ki being compact Hausdorff spaces) admits a Riesz type integral representation T(f1, . . . , fk) := Z (f1, . . . , fk) d, where is the representing polymeasure of T, i.e., a set function defined on the product of the Borel -algebras Bo(Ki) with values in X which is separately finitely additive. As in the linear case, the interplay between T and its representing polymeasure plays an important role. The aim of this paper is to survey some features of this relationship.