Perturbation Analysis for the Drazin Inverses of Bounded Linear Operators on a Banach Space
Guoliang Chen · Journal of Mathematical Research and Exposition · 2004
Let X be a Banach space over the complex field C and let T : X→X be a bounded linear operator with Ind(T) = k and R(Tk) closed. Denote the Drazin inverse of T by TD. Let T = T + δT, then TD has the simple expression TD = TD(I + δTTD)-1 = (I + TDδT)-1TD under certain hypotheses. The upper bound for the relative error ‖TD-TD‖/‖TD‖and for the solution to the operator equation: Tx = u (u∈R(TD)) is also considered.