Continuous multilinear operators on C(K) spaces and polymeasures
ISSN: 0213-8743
Any de publicació: 2007
Títol de l'exemplar: Banach space theory: classical topics and new directions. Cáceres 2006
Volum: 22
Número: 2
Pàgines: 127-146
Tipus: Article
Altres publicacions en: Extracta mathematicae
Resum
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.