TY - JOUR
T1 - On individual ergodic theorems for semifinite von Neumann algebras
AU - Chilin, Vladimir
AU - Litvinov, Semyon
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2021/3/1
Y1 - 2021/3/1
N2 - It is known that, for a positive Dunford-Schwartz operator in a noncommutative Lp-space, 1≤p<∞, or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge bilaterally almost uniformly. We show that these averages converge blaterally almost uniformly in each noncommutative symmetric space E such that μt(x)→0 as t→∞ for every x∈E, where μt(x) is the non-increasing rearrangement of x. Noncommutative Dunford-Schwartz-type multiparameter ergodic theorems are studied. A wide range of noncommutative symmetric spaces for which Dunford-Schwartz-type individual ergodic theorems hold is outlined.
AB - It is known that, for a positive Dunford-Schwartz operator in a noncommutative Lp-space, 1≤p<∞, or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge bilaterally almost uniformly. We show that these averages converge blaterally almost uniformly in each noncommutative symmetric space E such that μt(x)→0 as t→∞ for every x∈E, where μt(x) is the non-increasing rearrangement of x. Noncommutative Dunford-Schwartz-type multiparameter ergodic theorems are studied. A wide range of noncommutative symmetric spaces for which Dunford-Schwartz-type individual ergodic theorems hold is outlined.
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U2 - 10.1016/j.jmaa.2020.124710
DO - 10.1016/j.jmaa.2020.124710
M3 - Article
AN - SCOPUS:85094564441
SN - 0022-247X
VL - 495
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 124710
ER -