Most Markov operators on C(X) are quasi-compact and uniquely ergodic

Ryszard Rębowski

Displaying similar documents to “Most Markov operators on C(X) are quasi-compact and uniquely ergodic”

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Let P₁, ..., P_d be commuting Markov operators on L_∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each P_i is either conservative or invertible, we prove that for every f in L_p(X,F,μ) with 1 ≤ p < ∞ the averages A_nf = (n + 1)^-d Σ_{0≤n_i≤n} P₁