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

Dunford-Pettis and Compact Operators Based on Unbounded Absolute Weak Convergence