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 aτ on l p (g) has a 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 aτ on l p (g). for this purpose, we show that aτ is a lamperti operator. then we find a formula for its symbols τ . according to this formula, a representation for the symbol of adjoint and products is given.