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PERTURBATION ANALYSIS OF THE MOORE-PENROSE INVERSE FOR A CLASS OF BOUNDED OPERATORS IN HILBERT SPACES

Chunyuan Deng|Yimin Wei
대한수학회 (The Korean Mathematical Society)|2010.07|대한수학회지 (Journal of the KMS)|제47권 제4호|pp. 831-843

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참고문헌

키워드

perturbationMoore-Penrose inversegeneralized inverseblock operator matrix
주제분류수학

초록

Let H and K be Hilbert spaces and let T,T = T+δTbe bounded operators from H into K. In this article, two facts related to the perturbation bounds are studied. The first one is to find the upper bound of ∥T+T − T+T∥, which extends the results obtained by the second author and enriches the perturbation theory for the Moore-Penrose inverse. The other one is to develop explicit representations of projectors ∥T+T − T+T∥and ∥T+T − T+T∥. In addition, some spectral cases related to these results are analyzed.

Abstract

Let H and K be Hilbert spaces and let T,T = T+δTbe bounded operators from H into K. In this article, two facts related to the perturbation bounds are studied. The first one is to find the upper bound of ∥T+T − T+T∥, which extends the results obtained by the second author and enriches the perturbation theory for the Moore-Penrose inverse. The other one is to develop explicit representations of projectors ∥T+T − T+T∥and ∥T+T − T+T∥. In addition, some spectral cases related to these results are analyzed.

참고문헌 (21)

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