Hilbert空间中稳定扰动下广义逆的误差估计界

Error Estimate Bounds of Generalized Inverses under Stable Perturbation in Hilbert Spaces

设H1,H2 是两个复数域C上的Hilbert空间 ,T :H1→H2 是有界线性算子且有广义逆T+。令 T=T+δT且‖T+‖‖δT‖ <1,在稳定扰动意义下 (即R( T) ∩R(T) ⊥ =0 ) ,给出了‖ T+ T-T+T‖和‖ T+-T+‖的误差界。该文的结论推广、改进或简化了文献 [2 ][3][4 ][6 ]和 [9]中的相关结果或条件 。

Let H 1, H 2 be two Hilbert spaces over the complex field C and let T: H 1→H 2 be a bounded linear operator with the generalized inverse T + . Suppose =T+δT be a bounded linear operator with ‖T +‖‖δT‖<1 . Under assumption stable perturbation (i.e., R()∩R(T) ⊥= 0), we give the error bounds of ‖ +-T +T‖ and ‖ +-T +‖ . It generalize, improve or simplifies the relative results or conditions in references . Moreover, we also get useful four equivalent propositions for rectangular matrices.