Toying with Jordan matrices (Q1378082)

A bounded linear operator \(T\) defined on a Banach space is said to satisfy the ``resolvent estimate'' property if its resolvent set contains the negative reals, and there exists a constant \(\gamma>0\) such that the inequality \(\|(sI+ T)^{-1}\|\leq\gamma/s\) holds for all positive real \(s\). The author shows by means of an example that the resolvent estimate property is unstable under small perturbations.