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Journal of the Korean Mathematical Society = 대한수학회지 v.47 no.4, 2010년, pp.831 - 843   SCIE SCOPUS
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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  );
  • 초록

    Let $\cal{H}$ and $\cal{K}$ be Hilbert spaces and let T, $\tilde{T}$ = T + <TEX> 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.


  • 주제어

    generalized inverse .   Moore-Penrose inverse .   perturbation .   block operator matrix.  

  • 참고문헌 (21)

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