Ergodic theorems in fully symmetric spaces of τ-measurable operators

Vladimir Chilin, and Semyon Litvinov. "Ergodic theorems in fully symmetric spaces of τ-measurable operators." Studia Mathematica 228.2 (2015): 177-195. <http://eudml.org/doc/285884>.

@article{VladimirChilin2015,
abstract = {Junge and Xu (2007), employing the technique of noncommutative interpolation, established a maximal ergodic theorem in noncommutative $L_\{p\}$-spaces, 1 < p < ∞, and derived corresponding maximal ergodic inequalities and individual ergodic theorems. In this article, we derive maximal ergodic inequalities in noncommutative $L_\{p\}$-spaces directly from the results of Yeadon (1977) and apply them to prove corresponding individual and Besicovitch weighted ergodic theorems. Then we extend these results to noncommutative fully symmetric Banach spaces with the Fatou property and nontrivial Boyd indices, in particular, to noncommutative Lorentz spaces $L_\{p,q\}$. Norm convergence of ergodic averages in noncommutative fully symmetric Banach spaces is also studied.},
author = {Vladimir Chilin, Semyon Litvinov},
journal = {Studia Mathematica},
keywords = {semifinite von Neumann algebra; maximal ergodic inequality; noncommutative ergodic theorem; bounded Besicovitch sequence},
language = {eng},
number = {2},
pages = {177-195},
title = {Ergodic theorems in fully symmetric spaces of τ-measurable operators},
url = {http://eudml.org/doc/285884},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Vladimir Chilin
AU - Semyon Litvinov
TI - Ergodic theorems in fully symmetric spaces of τ-measurable operators
JO - Studia Mathematica
PY - 2015
VL - 228
IS - 2
SP - 177
EP - 195
AB - Junge and Xu (2007), employing the technique of noncommutative interpolation, established a maximal ergodic theorem in noncommutative $L_{p}$-spaces, 1 < p < ∞, and derived corresponding maximal ergodic inequalities and individual ergodic theorems. In this article, we derive maximal ergodic inequalities in noncommutative $L_{p}$-spaces directly from the results of Yeadon (1977) and apply them to prove corresponding individual and Besicovitch weighted ergodic theorems. Then we extend these results to noncommutative fully symmetric Banach spaces with the Fatou property and nontrivial Boyd indices, in particular, to noncommutative Lorentz spaces $L_{p,q}$. Norm convergence of ergodic averages in noncommutative fully symmetric Banach spaces is also studied.
LA - eng
KW - semifinite von Neumann algebra; maximal ergodic inequality; noncommutative ergodic theorem; bounded Besicovitch sequence
UR - http://eudml.org/doc/285884
ER -