Narrow operators on lattice-normed spaces
Functional Analysis
2013-09-24 v1
Abstract
The aim of this article is to extend results of Maslyuchenko O., Mykhaylyuk V. Popov M. about narrow operators on vector lattices. We give a new definition of a narrow operator where a vector lattice as the domain space of a narrow operator is replaced with a lattice-normed space. We prove that every GAM-compact (bo)-norm continuous linear operator from a Banach-Kantorovich space V to a Banach lattice Y is narrow. Then we show that, under some mild conditions, a continuous dominated operator is narrow if and only if its exact dominant is narrow.
Cite
@article{arxiv.1309.5490,
title = {Narrow operators on lattice-normed spaces},
author = {M. Pliev},
journal= {arXiv preprint arXiv:1309.5490},
year = {2013}
}