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On the pointwise entangled ergodic theorem (1509.05554v4)
Published 18 Sep 2015 in math.DS and math.FA
Abstract: We present some twisted compactness conditions for almost everywhere convergence of one-parameter entangled ergodic averages of Dunford-Schwartz operators $T_0,\ldots, T_a$ on a Borel probability space of the form $$ \sum_{n=1}N T_an A_{a-1}T_{a-1}nA_{a-1}\cdot \ldots \cdot A_0 T_0nf$$ for $f\in Lp(X,\mu)$, $p\geq 1$. We also discuss examples and present a continuous version of the result.