  In this paper, using the concept of unbounded absolute weak convergence
($uaw$-convergence, for short) in a Banach lattice, we define two classes of
continuous operators, named $uaw$-Dunford-Pettis and $uaw$-compact operators.
We investigate some properties and relations between them. In particular, we
consider some hypotheses on domain or range spaces of operators such that the
adjoint or the modulus of a $uaw$-Dunford-Pettis or $uaw$-compact operator
inherits a similar property. In addition, we look into some connections between
compact operators, weakly compact operators, and Dunford-Pettis ones with
$uaw$-versions of these operators. Moreover, we examine some relations between
$uaw$-Dunford-Pettis operators, $M$-weakly compact operators, $L$-weakly
compact operators, and $o$-weakly compact ones. As a significant outcome, we
show that the square of any positive $uaw$-Dunford-Pettis ($M$-weakly compact)
operator on an order continuous Banach lattice is compact. Many examples are
given to illustrate the essential conditions, as well.
