대한수학회지 (Journal of the Korean Mathematical Society)

  • 제47권4호
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  • Pages.831-843
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  • 2010
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2008.10.04
  • 발행 : 2010.07.01
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초록

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.

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참고문헌

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피인용 문헌

  1. Γ-inverses of bounded linear operators vol.30, pp.4, 2014, https://doi.org/10.1007/s10114-013-2552-y