Published online by Cambridge University Press: 20 January 2009
Throughout the paper, T will be a Markov operator on C(X) (X compact T2), i.e. a continuous positive operator such that Te = e (e the unit function). P will be the set of Borel probability measures on X, which we shall often think of as linear functionals on C(X), and , where T' is the adjoint of T. Let