Perturbation, interpolation, and maximal regularity (Q2434039)

The aim of this paper is to deduce perturbation theorems for sectoriality and \(R\)-sectoriality in Banach spaces. The authors consider a sectorial (or \(R\)-sectorial) operator \(A\) in a Banach space \(X\) and provide conditions on intermediate spaces \(Z\) and \(W\) such that for an operator \(S : Z \to W\) of sufficiently small norm, the perturbed operator \(A+S\) is sectorial (or \(R\)-sectorial). The authors illustrate their theory by several interesting examples.