Ergodic Properties of the Fröbenius–Perron Semigroup

Abstract

We consider the Fröbenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological space \(X\) endowed with a finite or a \(\sigma-\)finite regular measure. Assuming strong continuity for the Fröbenius-Perron semigroup of linear operators in the space \(L^1_\mu(X)\) or in the space \(L^p_\mu(X)\) for \(1 < p < \infty\) ([11]). We study in this article ergodic properties of the Fröbenius--Perron semigroup of linear operators.