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We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khinchin's recurrence theorem obtained by Bergelson in the measure-theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary.
Rocco Duvenhage. "Bergelson's theorem for weakly mixing C*-dynamical systems." Studia Mathematica 192.3 (2009): 235-257. <http://eudml.org/doc/284408>.
@article{RoccoDuvenhage2009, abstract = {We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khinchin's recurrence theorem obtained by Bergelson in the measure-theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary.}, author = {Rocco Duvenhage}, journal = {Studia Mathematica}, keywords = {nonconventional ergodic average; recurrence; weakly mixing -dynamical system; asymptotic abelian; -dynamical system}, language = {eng}, number = {3}, pages = {235-257}, title = {Bergelson's theorem for weakly mixing C*-dynamical systems}, url = {http://eudml.org/doc/284408}, volume = {192}, year = {2009}, }
TY - JOUR AU - Rocco Duvenhage TI - Bergelson's theorem for weakly mixing C*-dynamical systems JO - Studia Mathematica PY - 2009 VL - 192 IS - 3 SP - 235 EP - 257 AB - We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khinchin's recurrence theorem obtained by Bergelson in the measure-theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary. LA - eng KW - nonconventional ergodic average; recurrence; weakly mixing -dynamical system; asymptotic abelian; -dynamical system UR - http://eudml.org/doc/284408 ER -