Narrow operators on lattice-normed spaces and vector measures
Functional Analysis
2015-08-18 v1
Abstract
We consider linear narrow operators on lattice-normed spaces. We prove that, under mild assumptions, every finite rank linear operator is strictly narrow (before it was known that such operators are narrow). Then we show that every dominated, order continuous linear operator from a lattice-normed space over atomless vector lattice to an atomic lattice-normed space is order narrow.
Cite
@article{arxiv.1508.03995,
title = {Narrow operators on lattice-normed spaces and vector measures},
author = {D. T. Dzadzaeva and M. A. Pliev},
journal= {arXiv preprint arXiv:1508.03995},
year = {2015}
}