The generalized condition numbers of bounded linear operators in Banach spaces

For any bounded linear operator A in a Banach space, two generalized condition numbers (kappa) over bar (A) and (kappa) over cap (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.