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Traceability of positive integral operators in the absence of a metric. (English) Zbl 1272.47057

The traceability of positive integral operators on \(L^{2}(X,\mu)\) is investigated when \(X\) is a Hausdorff locally compact second countable space and is a non-degenerate, \(\sigma\)-finite and locally finite Borel measure. This setting includes other cases considered in the literature, for instance the one in which \(X\) is a compact metric space and \(\mu\) is a spatial finite measure. The results obtained here also apply to spheres, tori and other relevant subsets of the usual space \(\mathbb{R}^{m}\).

MSC:

47G10 Integral operators
47B34 Kernel operators
47B65 Positive linear operators and order-bounded operators
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
42A82 Positive definite functions in one variable harmonic analysis
60G46 Martingales and classical analysis
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References:

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