Banach空间上有界线性算子的Drazin逆的扰动分析(英文)

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

中文关键词:  Drazin逆  指标  误差界

英文关键词:Drazin inverse  index  error bound.

中文摘要:

      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<

英文摘要:

      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(T^k) closed. Denote the Drazin inverse of T by T^D. Let T = T + δT, then T^D has the simple expression T^D = T^D(I + δTT^D)^-1= (I + T^DδT)^-1T^D under certain hypotheses. The upper bound for the relative error ‖T^D-T^D‖/‖T^D‖and for the solution to the operator equation: Tx = u (u∈R(T^D)) is also considered.