It is well known that the upper bounds of the weighted Moore–Penroseinverseplay a fundamental role in the perturbation analysis for the weighted linear least squares problem. In this talk, we provide a sharp estimation. Thus norm estimations for the weighted Moore–Penrose inverses of theacute perturbations can be improved uniformly. Let  be the set of bounded linear operators on aBanach space , and a liner operator   be Drazin invertible.  and   arethe spectral projectors of   and  respectively. Some new formulas for spectral radius of   is generalized to the Banach space.