Ergodic properties of pseudo-differential operators on compact Lie groups

Let G be a compact Lie group. This article shows that a contraction pseudo-differential operator A(tau) on L-p(G) has Dominated Ergodic Estimate (DEE), and is trigonometrically well-bounded. Then we express ergodic generalization of the Vector-Valued M. Riesz theorem for invertible contraction pseudo-differential operator A(tau) on L-p(G). For this purpose, we show that A(tau) is a Lamperti operator. Then we find a formula for its symbols tau. According to this formula, a representation for the symbol of adjoint and products is given.