Almost everywhere convergence of entangled ergodic averages

2015/11/04 by Kunszenti-Kovács, Dávid
#37A30 (Secondary) #47A35 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1511.01528

Abstract

We study pointwise convergence of entangled averages of the form (1)/(N^k)∑_{1≤ n1,…, nk≤ N} T_m^n_α(m)A_m-1T^n_α(m-1)m-1… A₂T₂^n_α(2)A₁T₁^n_α(1) f, where f∈ L²(X,μ), α:\1,…,m\→\1,…,k\, and the T_i are ergodic measure preserving transformations on the standard probability space (X,μ). We show that under some joint boundedness and twisted compactness conditions on the pairs (A_i,T_i), almost everywhere convergence holds for all f∈ L². We also present results for the general L^p case (1≤ p

Related

• Norm convergence of multiple ergodic averages for commuting transformations
• Convergence of weighted ergodic averages
• On the entangled ergodic theorem
• The entangled ergodic theorem in the almost periodic case
• Strictly ergodic models and the convergence of non-conventional pointwise ergodic averages