Convergence of generic infinite products of homogeneous order-preserving mappings
This article deals with the asymptotic behaviour of (random) products of a generic sequence \(\{A_t\}^\infty_{t=1}\) of homogeneous order-preserving mappings \(A_t\) on a cone \(X_+\) in an ordered Banach space \(X\). The basic results (7 Theorems) are concerned with the existence of a set \({\mathcal F}\) which is a countable intersection of open everywhere dense sets in suitable spaces of sequences, on the one hand, and each element of which has the prescribed asymptotic behaviour together with elements of some neighbourhood, on the other. These results can be considered as modifications of the weak ergodic theorem; some of them state even the convergence of the corresponding infinite products to an operator of type \(f(\cdot)\eta\) where \(f\) is a functional and \(\eta\) a common fixed point of mappings from the considered sequence.
scientific article; zbMATH DE number 1492599