It is well known that for an associative ring R, if ab has g-Drazin inverse
then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula
is so-called Cline?s formula for g-Drazin inverse, which plays an elementary
role in matrix and operator theory. In this paper, we generalize Cline?s
formula to the wider case. In particular, as applications, we obtain new
common spectral properties of bounded linear operators.