This is an announcement for the paper "Iterations of the projection body operator and a remark on Petty's conjectured projection inequality" by Christos Saroglou and Artem Zvavitch. Abstract: We prove that if a convex body has absolutely continuous surface area measure, whose density is sufficiently close to the constant, then the sequence $\{\Pi^mK\}$ of convex bodies converges to the ball with respect to the Banach-Mazur distance, as $m\rightarrow\infty$. Here, $\Pi$ denotes the projection body operator. Our result allows us to show that the ellipsoid is a local solution to the conjectured inequality of Petty and to improve a related inequality of Lutwak. Archive classification: math.MG math.FA Remarks: 13 pages Submitted from: csaroglo@kent.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1511.03381 or http://arXiv.org/abs/1511.03381