Moore-Penrose逆的可微性

讨论了Hibert空间H1到H2有界线性算子全体构成的Banach空间LH1,H2上Moore-Penrose逆的连续性和可微性,给出了函数T+t在一点可微的几个等价描述,同时得到一个求导公式.所得的结果推广了Golub和Pereyra早期的主要结果.

Differentiability of Moore-Penrose Inverse

Let H1,H2 be two Hiberts spaces over the complex field,and let L H1,H2 denote the Banach space of all bounded linear operations T: H1 → H2 with the operator norm T = sup Tx : x = 1.Let a,b be an interval with be an element of a,b,and T t be an operator valuedfunctiondefinedfor all t a,b].By T' t denotethederivativeof T t at t,and by T+(t) denote the Moore-penrose inverse T t + of T t.The continuity and differentiability of the Moore-penrose inverse in L(H1,H2) is investigated.Some necessary and sufficient conditions for the function is differentiable at t0 are given.A formula for derivative(T+)i′s derived.The main results of Golub and Pereyra in 4] generalized to the case of operators in Hibert spaces.