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Pointwise entangled ergodic theorems for Dunford-Schwartz operators | | Dávid Kunszenti-Kovács
; | | Date: |
22 May 2017 | | Abstract: | We investigate pointwise convergence of entangled ergodic averages of
Dunford-Schwartz operators $T_0,T_1,ldots, T_m$ on a Borel probability space.
These averages take the form [ frac{1}{N^k}sum_{1leq n_1,ldots, n_kleq N}
T_m^{n_{alpha(m)}}A_{m-1}T^{n_{alpha(m-1)}}_{m-1}ldots
A_2T_2^{n_{alpha(2)}}A_1T_1^{n_{alpha(1)}} f, ] where $fin L^p(X,mu)$ for
some $1leq p<infty$, and
$alpha:left{1,ldots,m
ight} oleft{1,ldots,k
ight}$ encodes the
entanglement. We prove that under some joint boundedness and twisted
compactness conditions on the pairs $(A_i,T_i)$, almost everywhere convergence
holds for all $fin L^p$. We also present an extension to polynomial powers in
the case $p=2$, in addition to a continuous version concerning Dunford-Schwartz
$C_0$-semigroups. | | Source: | arXiv, 1705.7693 | | Services: | Forum | Review | PDF | Favorites | |
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