The generalized condition numbers of bounded linear operators in Banach spaces

Abstract

For any bounded linear operator A in a Banach space, two generalized condition numbers κ̄ (A) and κ̂(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.