Nuclear operators on Banach function spaces
The author investigates nuclear operators on Banach function spaces. Among other interesting results, it is proved that every nuclear operator \(T:E\longrightarrow X\) between the locally convex space \((E,\tau(E,E^{\prime }))\) and a Banach space \(X\) is Bochner representable, where \(E\) is an order ideal of \(L^{0}\) such that \(L^{\infty }\subset E\subset L^{1}\), with a Riesz norm \(\left\Vert \cdot \right\Vert _{E}\). Especially, if \( E=L^{\infty }\), then the operator \(T\) is nuclear if and only if its representing measure has the Radon-Nikodym property and admits a factorization through some Orlicz space.
scientific article; zbMATH DE number 7382072
scientific article