POINTWISE ERGODIC THEOREMS FOR BOUNDED LAMPERTI REPRESENTATIONS OF AMENABLE GROUPS.

Dominated and Pointwise Ergodic Theorems for bounded representations of second countable locally compact amenable groups by Lamperti operators in L^p(O,F,m), p > 1 fixed, are proved; we restrict ourselves to Cesàro averages in this paper. These theorems generalize or are closely related to well-known theorems for powers of power bounded Lamperti operators. [ABSTRACT FROM AUTHOR]