  We show that every dominated linear operator from an Banach-Kantorovich space
over atomless Dedekind complete vector lattice to a sequence Banach lattice
$l_p({\Gamma})$ or $c_0({\Gamma})$ is narrow. As a conse- quence, we obtain
that an atomless Banach lattice cannot have a finite dimensional decomposition
of a certain kind. Finally we show that if a linear dominated operator T from
lattice-normed space V to Banach- Kantorovich space W is order narrow then the
same is its exact dominant $\ls T\rs$.
