Journal of the Australian Mathematical Society
- Journal of the Australian Mathematical Society / Volume 76 / Issue 02 / April 2004, pp 281-290
- Copyright © Australian Mathematical Society 2004
- DOI: http://dx.doi.org/10.1017/S1446788700008958 (About DOI), Published online: 09 April 2009
Research Article
The generalized condition numbers of bounded linear operators in Banach spaces
Guoliang Chena1, Yimin Weia2 and Yifeng Xuea3
a1 Department of Mathematics, East China Normal University, Shanghai, 200062 P.R., China
a2 Department of Mathematics, Fudan University Shanghai 200433 P. R., China
a3 Department of Mathematics, East China University of Science and Technology, Shanghai 200237 P.R., China e-mail: xyf63071@public9.sta.net.cn
Abstract
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.
(Received May 01 2002)
(Revised March 03 2003)
2000 Mathematics subject classification
- primary 47A05;
- 65F20;
- 65J1
Keywords and phrases
- Condition number;
- bounded linear operator;
- generalized inverse
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