Banach空间上有界线性算子的Drazin逆的扰动分析

设X为一复域C上的Banach空间,设T:X→X为一有界线性算子,其指标为k且R(T^k)闭.记T的Drazin逆为T^D.设T=T+δT,则在一定条件下,T^D有简明分解式T^D=T^D(I+δTT^D)^-1=(I+T^DδT)^-1T^D,从而导出了相对误差‖T^D-T^D<

Perturbation Analysis for the Drazin Inverses of Bounded Linear Operators on a Banach Space

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(Tκ) 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.