Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Characterization of some classes of operators on spaces of vector-valued continuous functions

Fernando Bombala1 and Pilar Cembranosa1

a1 Departamento de Teoría de Funciones, Universidad Complutense de Madrid, Spain

Let K be a compact Hausdorff space and E, F Banach spaces. We denote by C(K, E) the Banach space of all continuous. E-valued functions defined on K, with the supremum norm. It is well known ([6], [7]) that every operator (= bounded linear operator) T from C(K, E) to F has a finitely additive representing measure m of bounded semi-variation, defined on the Borel σ-field Σ of K and with values in L(E, F″) (the space of all operators from E into the second dual of F), in such a way that


where the integral is considered in Dinculeanu's sense.

(Received April 26 1984)