This is an announcement for the paper "Narrow operators on lattice-normed spaces and vector measures" by D.T. Dzadzaeva and M.A. Pliev.
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.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B99, Secondary 46G12
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/1508.03995
or