Perturbation Analysis of the AlgebraicMetric Generalized Inverse in Lp(Ω,µ).

Let X = L^p(Ω,μ) (1<p<∞) and T,δT:X→X be bounded linear operators. Put T = T + δT. In this paper, using the notion of quasi-additivity and the concept of stable perturbation, we will give some estimates of the upper bound of T^M - T^M in terms of the gap function. As an application of main results, we also investigate the best approximate solution problem of ill-posed operator equation. [ABSTRACT FROM AUTHOR]