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The generalized condition numbers of bounded linear operators in Banach spaces

Published online by Cambridge University Press:  09 April 2009

Guoliang Chen
Department of Mathematics, East China Normal University, Shanghai, 200062 P.R., China
Yimin Wei
Department of Mathematics, Fudan UniversityShanghai 200433 P. R., China
Yifeng Xue
Department of Mathematics, East China University of Science and Technology, Shanghai 200237 P.R., China e-mail:
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For any bounded linear operator A in a Banach space, two generalized condition numbers, k(A) and k(A) are defined in this paper. These condition numbers may be applied to the perturbation analysis for the solution of ill-posed differential equations and bounded linear operator equations in infinite dimensional Banach spaces. Different expressions for the two generalized condition numbers are discussed in this paper and applied to the perturbation analysis of the operator equation.

Research Article
Copyright © Australian Mathematical Society 2004


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