A Perron-Frobenius theorem for positive polynomial operators in Banach lattices

In this paper, we extend the Perron-Frobenius theorem for positive polynomial operators in Banach lattices. The result obtained is applied to derive necessary and sufficient conditions for the stability of positive polynomial operators. Then we study stability radii: complex, real and positive radii of positive polynomial operators and show that in this case the three radii coincide and can be computed by a simple formula. Finally, a simple example is given to illustrate the obtained results.