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

Published online by Cambridge University Press:  24 October 2008

Fernando Bombal  and
Pilar Cembranos
Fernando Bombal
Affiliation:
Departamento de Teoría de Funciones, Universidad Complutense de Madrid, Spain
Pilar Cembranos
Affiliation:
Departamento de Teoría de Funciones, Universidad Complutense de Madrid, Spain
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 137 - 146
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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