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Winter 2003 On the Expression of Generalized Inverses of Perturbed Bounded Linear Operators
Jiu Ding
Missouri J. Math. Sci. 15(1): 40-47 (Winter 2003). DOI: 10.35834/2003/1501040

Abstract

Let $X$ and $Y$ be two Hilbert spaces or Banach spaces, and let $T \colon X \rightarrow Y$ be a bounded linear operator with closed range. Let $\tilde{T} = T + \delta T$ with $\|\delta T\| \|T^{\dagger}\| < 1$. We give some equivalent conditions for the generalized inverse of $\tilde{T}$ to have the simplest expression $\tilde{T}^{\dagger} = (I + T^{\dagger}\delta T)^{-1} T^{\dagger} = T^{\dagger} (I + \delta T T^{\dagger})^{-1}$.

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Jiu Ding. "On the Expression of Generalized Inverses of Perturbed Bounded Linear Operators." Missouri J. Math. Sci. 15 (1) 40 - 47, Winter 2003. https://doi.org/10.35834/2003/1501040

Information

Published: Winter 2003
First available in Project Euclid: 31 August 2019

zbMATH: 1039.47001
MathSciNet: MR1959068
Digital Object Identifier: 10.35834/2003/1501040

Rights: Copyright © 2003 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.15 • No. 1 • Winter 2003
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