Dominated operators from lattice-normed spaces to sequence Banach lattices

Abstract. We show that every dominated linear operator from a Banach-Kantorovich space over an atomless Dedekind-complete vector lattice to a sequence Banach lattice ℓp(Γ) or c0(Γ) is narrow. As a consequence, we obtain that an atomless Banach lattice cannot have a finite-dimensional decomposition of a certain kind. Finally, we show that the order-narrowness of a linear dominated operator T from a lattice-normed space V to the Banach space with a mixed norm (W, F) over an order-continuous Banach lattice F implies the order-narrowness of its exact dominant |T|. © 2016 by the Tusi Mathematical Research Group.