Necessary and sufficient conditions for invertibility of operators in spaces of real interpolation (Q1932404)

The authors give necessary and sufficient conditions in order that an operator which is invertible at the ends of an interpolation pair is invertible on a real interpolation space of the pair. The main result is Theorem 1: An operator \(A\) is invertible on the space \((X_{0}, X_{1})_{\theta, q}\) if and only if \[ \ker A=V_{\theta, q}^{0}\oplus V_{\theta, q}^{1} \] and \[ \beta(V_{\theta, q}^{1})<\theta<\alpha(V_{\theta, q}^{0}). \] In my opinion, this is a nice piece of work.