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Integral representations for a class of operators
Authors:Surjit Singh Khurana
Institution:Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
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, View the MathML source, View the MathML source. 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 gf=0 for any fCb(X,E), gE.
Keywords:Strict topologies  Separable measures  Tight measures  τ-Smooth measures
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