  Suppose $X$ is a locally solid vector lattice. It is known that there are
several non-equivalent spaces of bounded operators on $X$. In this paper, we
consider some situations under which these classes of bounded operators form
locally solid vector lattices. In addition, we generalize some notions of
$uaw$-Dunford-Pettis operators and $uaw$-compact operators defined on a Banach
lattice to general theme of locally solid vector lattices. With the aid of
appropriate topologies, we investigate some relations between topological and
lattice structures of these operators. In particular, we characterize those
spaces for which these concepts of operators and the corresponding classes of
bounded ones coincide.
