A max version of the generalized spectral radius theorem

Let Psi be a bounded set of n x n nonnegative matrices in max algebra. In this paper we propose the notions of the max algebra version of the generalized spectral radius mu(Psi) of Psi, and the max algebra version of the joint spectral radius eta(Psi) of Psi. The max algebra version of the generalized spectral radius theorem mu(Psi) = eta(Psi) is established. We propose the relationship between the generalized spectral radius rho(Psi) of Psi (in the sense of Daubechies and Lagarias) and its max algebra version mu(Psi). Moreover, a generalization of Elsner and van den Driessche's lemma is presented as well. (c) 2006 Elsevier Inc. All rights reserved.