关于Moore-Penrose逆T^+连续性的一个注(英文)

A Note on the Continuity of Moore-Penrose Inverses T^+

设X为拓扑空间.H1和H2为Hilbert空间,T(·)为X到B(H1,H2)的连续映射.本文主要利用Tikhonov正则化算子给出了Moore-Penrose逆T+x连续的充分必要条件.这个结果在计算数学中是很重要的.

Let X be a topological space. Let H1 and H2 be two Hilbert spaces and T（-） be a continuous mapping from X into B（H1 , H2 ）. In this paper, using the Tickhonov regularizer, we give a sufficient and necessary condition for the Moore-Penrose inverses Tx^＋ being continuous, which plays an important role in the computation.