Integral representations for a class of operators |
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Authors: | Surjit Singh Khurana |
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Institution: | Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA |
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Abstract: | Let X be a completely regular Hausdorff space, E Hausdorff a quasi-complete locally convex space and Cb(X,E) all E-valued bounded continuous functions on X with strict topologies βt, , . We prove that a linear continuous mapping T:Cb(X,E)→E arises from a scalar measure μ∈(Cb′(X),βz)(z=t,∞,τ) if and only if g(T(f))=0 whenever g○f=0 for any f∈Cb(X,E), g∈E′. |
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Keywords: | Strict topologies Separable measures Tight measures τ-Smooth measures |
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