Traceability of positive integral operators in the absence of a metric

TL;DR

This paper studies conditions under which positive integral operators are traceable on certain function spaces without requiring a metric, extending previous results to more general topological spaces.

Contribution

It extends the traceability results of positive integral operators to Hausdorff locally compact second countable spaces without metric assumptions.

Findings

Established traceability criteria in non-metric spaces

Included applications to spheres, tori, and subsets of Euclidean space

Generalized previous metric-based results

Abstract

We investigate the traceability of positive integral operators on $L^2(X,\mu)$ when $X$ is a Hausdorff locally compact second countable space and $\mu$ is a non-degenerate, $\sigma$-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 $\mu$ is a special finite measure. The results apply to spheres, tori and other relevant subsets of the usual space $\mathbb{R}^m$.