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The generalized condition numbers of bounded linear operators in Banach spaces

Part of: Numerical linear algebra General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Guoliang Chen ,
Yimin Wei  and
Yifeng Xue
Guoliang Chen
Affiliation:
Department of Mathematics, East China Normal University, Shanghai, 200062 P.R., China
Yimin Wei
Affiliation:
Department of Mathematics, Fudan UniversityShanghai 200433 P. R., China
Yifeng Xue
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai 200237 P.R., China e-mail: xyf63071@public9.sta.net.cn
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Abstract

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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.

Keywords

Condition numberbounded linear operatorgeneralized inverse

MSC classification

Secondary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 65F20: Overdetermined systems, pseudoinverses
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 2 , April 2004 , pp. 281 - 290
Copyright
Copyright © Australian Mathematical Society 2004

References

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