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Operators on locally convex spaces of vector-valued continuous functions

Published online by Cambridge University Press:  17 April 2009

A. García López
A. García López
Affiliation:
Departamento de Teoria de Funciones, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
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Abstract

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Let E and F be locally convex spaces and let K be a compact Hausdorff space. C(K,E) is the space of all E-valued continuous functions defined on K, endowed with the uniform topology.

Starting from the well-known fact that every linear continuous operator T from C(K,E) to F can be represented by an integral with respect to an operator-valued measure, we study, in this paper, some relationships between these operators and the properties of their representing measures. We give special treatment to the unconditionally converging operators.

As a consequence we characterise the spaces E for which an operator T defined on C(K,E) is unconditionally converging if and only if (Tfn) tends to zero for every bounded and converging pointwise to zero sequence (fn) in C(K,E).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 2 , October 1987 , pp. 267 - 278
Copyright
Copyright © Australian Mathematical Society 1987

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