We present new conditions under which Cline?s formula and Jacobson?s lemma for g-Drazin inverse hold. Let A be a Banach algebra, let a,b ? satisfying akbkak = ak+1 some k N. prove that has if only bkak inverse. In this case, (bkak)d bk(ad)2ak ad ak[(bkak)d]k+1. Further, we study in algebra the preceding condition. The common spectral property of bounded linear operators on space is thereby obta...
