2013/09/21 by Marat Pliev, Pliev, M.
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Primary 46B99 #Secondary 47B99
paper · pdf · doi:10.48550/arxiv.1309.5490
openalex publication_date 2013/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.