Nuclear operators and applications to kernel operators

Marian Nowak

Mathematische Nachrichten, 2023, vol. 296, issue 5, 2109-2120

Abstract: Let Σ be a σ‐algebra of subsets of a set Ω and B(Σ)$B(\Sigma )$ 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 m:Σ→E$m:\Sigma \rightarrow E$ of finite variation |m|(Ω)$|m|(\Omega )$ with a |m|$|m|$‐Bochner integrable derivative and nuclearity of the corresponding integration operator Tm:B(Σ)→E$T_m:B(\Sigma )\rightarrow E$. As an application, we derive that if Ω is a topological Hausdorff space and Y is a compact Hausdorff space and k∈Cb(Y×Ω)$k\in C_b(Y\times \Omega )$, then the corresponding kernel operator T:B(Bo)→C(Y)$T:B({\cal B}o)\rightarrow C(Y)$ is nuclear.

Date: 2023
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