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- W2252704206 abstract "The aim of this article is to extend results of M.~Popov and second named author about orthogonally additive narrow operators on vector lattices. The main object of our investigations are an orthogonally additive narrow operators between lattice-normed spaces. We prove that every $C$-compact laterally-to-norm continuous orthogonally additive operator from a Banach-Kantorovich space $V$ to a Banach lattice $Y$ is narrow. We also show that every dominated Uryson operator from Banach-Kantorovich space over an atomless Dedekind complete vector lattice $E$ to a sequence Banach lattice $ell_p(Gamma)$ or $c_0(Gamma)$ is narrow. Finally, we prove that if an orthogonally additive dominated operator $T$ from lattice-normed space $(V,E)$ to Banach-Kantorovich space $(W,F)$ is order narrow then the order narrow is its exact dominant $ls Trs$." @default.
- W2252704206 created "2016-06-24" @default.
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- W2252704206 date "2015-09-30" @default.
- W2252704206 modified "2023-09-22" @default.
- W2252704206 title "Narrow Orthogonally Additive Operators on Lattice-Normed Spaces" @default.
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