Traceability of positive integral operators in the absence of a metric

We investigate the traceability of positive integral operators on [L.sup.2](X,μ) when X is a Hausdorff locally compact second countable space and μ is a non-degenerate, σ-finite and locally finite Borel measure. This setting includes other cases proved in the literature, for instance the one in which X is a compact metric space and μ is a special finite measure. The results apply to spheres, tori and other relevant subsets of the usual space [R.sup.m].