This is an announcement for the paper "Domination by positive weak* Dunford-Pettis operators on Banach" by Jin Xi Chen, Zi Li Chen, and Guo Xing Ji. Abstract: Recently, J. H'michane et al. introduced the class of weak* Dunford-Pettis operators on Banach spaces, that is, operators which send weakly compact sets onto limited sets. In this paper the domination problem for weak* Dunford-Pettis operators is considered. Let $S, T:E\rightarrow F$ be two positive operators between Banach lattices $E$ and $F$ such that $0\leq S\leq T$. We show that if $T$ is a weak$^{*}$ Dunford-Pettis operator and $F$ is $\sigma$-Dedekind complete, then $S$ itself is weak* Dunford-Pettis. Archive classification: math.FA math.OA Mathematics Subject Classification: Primary 46B42, Secondary 46B50, 47B65 Remarks: 8 pages Submitted from: jinxichen@home.swjtu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.2808 or http://arXiv.org/abs/1311.2808