Reverse Order Law for the Drazin Inverse in Banach Spaces

We derive some equivalent conditions for the reverse order law (PQ)D=QDPD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(PQ)^D=Q^DP^D$$\end{document} to hold for Drazin invertible bounded linear operators P and Q. Moreover, the Drazin invertibility of sum is investigated for two bounded linear operators and the expression of Drazin inverse is presented. The results generalize some recent works.