Some Applications of Spectral Analysis to Ergodic Theory

Let X be a Banach Space and L [X, X] the space of continuous linear operators on X. For T ∈ L [X, X] let A_n = 1/n (T+ T² + . . . + Tⁿ), n = l,2, ... To discuss the convergence properties of {A_n} when T is a compact operator, Higgins [2] used spectral decomposition and the properties of collectively compact sets of operators.