On orthogonally additive operators in Köthe-Bochner spaces
The authors consider the narrowness of orthogonally additive operators in the Köthe-Banach spaces in the sense of [\textit{P.-K. Lin}, Köthe-Bochner function spaces. Boston, MA: Birkhäuser (2004; Zbl 1054.46003)]. They use the technique of domination as presented in [\textit{A. G. Kusraev}, Dominated operators. Transl. from the Russian by the author and edited by S. S. Kutateladze. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0983.47025)] to show that a dominated orthogonally additive operator \(T\) to a Banach lattice with \(o\)-continuous norm is narrow iff so is the exact dominant of \(T\). Some close results are also given.
scientific article; zbMATH DE number 7362286
scientific article