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

• Deng, Chunyuan (COLLEGE OF MATHEMATICS SCIENCE SOUTH CHINA NORMAL UNIVERSITY) ;
• Wei, Yimin (SCHOOL OF MATHEMATICAL SCIENCES FUDAN UNIVERSITY)
• Published : 2010.07.01

#### Abstract

Let $\cal{H}$ and $\cal{K}$ be Hilbert spaces and let T, $\tilde{T}$ = T + ${\delta}T$ be bounded operators from $\cal{H}$ into $\cal{K}$. In this article, two facts related to the perturbation bounds are studied. The first one is to find the upper bound of $\parallel\tilde{T}^+\;-\;T^+\parallel$ 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 $\parallel\tilde{T}\tilde{T}^+\;-\;TT^+\parallel$ and $\parallel\tilde{T}^+\tilde{T}\;-\;T^+T\parallel$. In addition, some spectral cases related to these results are analyzed.

#### Acknowledgement

Supported by : National Natural Science Foundation, Shaanxi Province Education Committee, National Natural Science Foundation of China, Shanghai Municipal Science & Technology Committee

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