Abstract

In this article, we estimate the spectral radius of linear bounded operators on Banach spaces when they are subjected to perturbations of the single or multi-block structured form. Then, we derive formulae and bounds for structured distance to non-invertibility (resp. non-left, non-right invertible operator) of an invertible (resp. left, right invertible) operator on Banach spaces. Some special cases of that estimate will also be considered.