Nuclear operators and applications to kernel operators

Abstract

AbstractLet Σ be a σ‐algebra of subsets of a set Ω and be the Banach lattice of bounded Σ‐measurable real functions on Ω. For a Banach space E, we establish the relationship between a countably additive measure of finite variation with a ‐Bochner integrable derivative and nuclearity of the corresponding integration operator . As an application, we derive that if Ω is a topological Hausdorff space and Y is a compact Hausdorff space and , then the corresponding kernel operator is nuclear.