Operators on locally convex spaces of vector-valued continuous functions
Copyright policy )Operators on locally convex spaces of vector-valued continuous functions
LetEandFbe locally convex spaces and letKbe a compact Hausdorff space.C(K,E) is the space of allE-valued continuous functions defined onK, endowed with the uniform topology.Starting from the well-known fact that every linear continuous operatorTfromC(K,E) toFcan 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 spacesEfor which an operatorTdefined onC(K,E) is unconditionally converging if and only if (Tfn) tends to zero for every bounded and converging pointwise to zero sequence (fn) inC(K,E).
s-bounded operator, Spaces of vector- and operator-valued functions, Linear operators on function spaces (general), operators on locally convex spaces of vector-valued continuous functions, unconditionally converging operators, Vector-valued measures and integration, representing measures
s-bounded operator, Spaces of vector- and operator-valued functions, Linear operators on function spaces (general), operators on locally convex spaces of vector-valued continuous functions, unconditionally converging operators, Vector-valued measures and integration, representing measures
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