Operational quantities derived from the minimum modulus

Manuel,Gonzáles ,Antonio,Martinón

The minimum modulus $\gamma(T)$ of an operator $T$ is useful in perturbation theory because it characterizes the operators with closed range. Here we study the operational quantities derived from $\gamma(T)$. We show that the behavior of some of these quantities depends largely on whether the null space of $T$ is finite dimensional or infinite dimensional.