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The generalized condition numbers of bounded linear operators in Banach spaces
Published online by Cambridge University Press: 09 April 2009
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.
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References
[1]Chen, G., ‘Minimum property in some problems with condition number of square matrices’, Comm. Appl. Math. Comput. 1 (1988), 74–80 (Chinese).Google Scholar
[2]Chen, G. and Chen, D., ‘On the minimum property of condition number for doubly perturbed linear equations’, J. Math. Applicata 3 (1989), 69–76 (Chinese).Google Scholar
[3]Chen, G. and Xue, Y., ‘Perturbation analysis for the operator equation Tx = b in Banach spaces’, J. Math. Anal. Appl. 212 (1997), 107–125.CrossRefGoogle Scholar
[4]Demko, S., ‘Condition numbers of rectangular systems and bounds for generalized inverses’, Linear Algebra Appl. 78 (1986), 199–206.CrossRefGoogle Scholar
[6]Dunford, N. and Schwartz, J. T., Linear operators. Part 3: Spectral operators (Wiley, New York, 1971).Google Scholar
[7]Kato, T., Perturbation theory for linear operators, 2nd edition (Springer, Berlin, 1984).Google Scholar
[8]Kuang, J., ‘The ω-condition number of linear operators’, Numer Math. J. Chinese Univ. 1 (1980), 11–18 (Chinese).Google Scholar
[9]Pragua, J. R., ‘New condition number for matrices and linear systems’, Computing 41 (1989), 211–213.Google Scholar
[11]Wolkowicz, H. and Zlobec, S., ‘Calculating the best approximate solution of an operator equation’, Math. Comp. 32 (1978), 1183–1213.CrossRefGoogle Scholar
[12] Xue, Y., ‘The reduced minimum modulus of elements in C*-algebras’, preprint.Google Scholar
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