J. Aust. Math. Soc.  76 (2004), 281-290
The generalized condition numbers of bounded linear operators in Banach spaces

Guoliang Chen
  Department of Mathematics
  East China Normal University
  Shanghai 200062
  P.R. China
 
Yimin Wei
  Department of Mathematics
  Fudan University
  Shanghai 200433
  P.R. China
 
and
Yifeng Xue
  Department of Mathematics
  East China University of
  Science and Technology
  Shanghai 200237
  P.R. China
  xyf63071@public9.sta.net.cn


Abstract
For any bounded linear operator $A$ in a Banach space, two generalized condition numbers $\bar{\kappa}(A)$ and $\hat{\kappa}(A)$ 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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