摘要
设X是一Banach空间 .B(X)表示XX的有界线性算子全体构成的向量空间 .T∈B(X) ,指标为k且R(Tk)闭 ,T =T +δT为T的扰动 ,记TD 为T的Drazin逆 ,则在R(δT) R(Tk) ,N(δT) N(Tk)及△ =‖TD‖‖δT‖ <1的条件下 ,有TD-TD 的简明分解式及相应的误差估计 .此外还给出了TD 的一个与Tk+ 有关的表达式 .作为应用 ,讨论了算子方程Tx =u(u∈R(TD) )
Let X be a Banach space. B(X) denotes the vector space of all bounded linear operators T:XX . Let T be T=T+δT∈B(X) . Suppose Ind( T)=k, R(T k ) is closed. Denote the Drazin inverse of T by T D . If R(δT)R(T k), N(δT)N(T k) and △ equals ‖ T D‖‖δT ‖<1, then we have a simple decomposition of T D-T D and its error estimate. Moreover, we also find an expression of T D with respect to the generalized inverse T k+ . This paper also discusses the upper bound for the solution to the operator equation: Tx=u(u∈R(T D) ).
出处
《湖州师范学院学报》
2001年第6期17-21,共5页
Journal of Huzhou University
