This is an announcement for the paper "Narrow Orthogonally Additive Operators on Lattice-Normed Spaces" by Xiao Chun Fang and Marat Pliev.

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 $\ls T\rs$.

Archive classification: math.FA

Mathematics Subject Classification: 46B99. 47B99

Remarks: 16 pages

Submitted from: martin.weber@tu-dresden.de

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1509.09189

or

http://arXiv.org/abs/1509.09189