Collatz-Wielandt numbers in general partially ordered spaces

AbstractIt has been shown by Förster and Nagy that the convergence of the Collatz-Wielandt numbers to bound the spectral radius of a K-nonnegative linear operator T in a partially ordered Bannach space essentially depends upon the starting vector of the iteration process. In this paper necessary and sufficient conditions for convergence are presented under rather general hypotheses; e.g., the emptiness of the interior of the order cone K is admitted. We also present min sup and max inf characterizations of the spectral radius in the spirit of earlier work