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Lamperti-type operators on a weighted space of continuous functions. (English) Zbl 0870.47019

Summary: For a locally convex Hausdorff topological vector space \(E\) and for a system \(V\) of weights vanishing at infinity on a locally compact Hausdorff space \(X\), let \(CV_0(X,E)\) be the weighted space of \(E\)-valued continuous functions on \(X\) with the locally convex topology derived from the seminorms which are weighted analogues of the supremum norm. A characterization of the orthogonality preserving (Lamperti-type) operators on \(CV_0(X,E)\) is presented in this paper.

MSC:

47B38 Linear operators on function spaces (general)
46E40 Spaces of vector- and operator-valued functions
47B60 Linear operators on ordered spaces
46E10 Topological linear spaces of continuous, differentiable or analytic functions
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