On the invertibility of bounded operators with a lower bound on reflexive Banach spaces, and applications to \(C_{0}\)-semigroups

Abstract

We present a new version of an invertibility result for operators satisfying a lower bound condition. The result states that any bounded operator on a reflexive Banach space, which satisfies the lower bound condition, can be extended to a larger reflexive Banach space where it becomes invertible. Furthermore, we provide applications to \(C_{0}\)-semigroups.