Abstract

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.

Keywords: Minimum modulus, perturbation theory.

MSC: 47A53

Pages:  1$-$5     

Volume  58 ,  Issue  1$-$2 ,  2006