首页 / 资料库 / 文献详情

AN APPROXIMATION THEOREM OF A M-P INVERSE BY OUTER INVERSES

马兆丰、Ma Pu

2004高等学校计算数学学报：英文版Computer Science被引 1

摘要

Let H1 and H2 be separable Hilbert spaces, and B(H1, H2) all of bounded linear operators from H1 into H2. In this note, we prove the following theorem: for any positive integer N and T ∈ B(H1, H2) with a closed range, there exists an outer inverse T#N with finite rank N such that T+y = lira T#Ny for any y ∈ H2, where T+N →∞denotes the Moore-Penrose inverse of T. Thus computing T+ is reduced to computing outer inverses T#N with finite rank N. Moreover, because of the stability of bounded outer inverse of a T ∈ B(H1,H2), this is very useful.

引用本文（GB/T 7714）