Uniform convergence of stochastic semigroups (Q2143223)

The authors do use the lattice structure and especially the notions of the quasi-interior point and the ideal generated by such a point in Lebasgue spaces, whose norm interior of the positive cone is empty, in order to study dynamical systems behaviour. Especially, the existence of quasi-interior points is associated to the erdodicity of such a dynamical system. A dynamical system is understood as a semigroup of integration operators acting on AL-Banach Lattices. Any element of such a semigroup maps any element of such a Banach Lattice to itself. The cardinality of these operators is equal to the continuum and the ergodidity is understoos as the behaviour of the 'mean' operator. Such a mean operator is ergodic if it is a bounded operator. Since AL-norm's properties are implied by the lattice structure of it, they are primarely assumed. The behaviour of such systems is associated to the implied differential operators' semigroup.This is a pure contribution in theory and applications of infinitesemal operators in physics and economic science.