Ergodic theorems in fully symmetric spaces of τ-measurable operators

2014/10/06 by Chilin, Vladimir, Litvinov, Semyon
#46L52(secondary) #47A35(primary) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1410.1451

Abstract

In [11], employing the technique of noncommutative interpolation, a maximal ergodic theorem in noncommutative Lp-spaces, 1 < p < infinity, was established and, among other things, corresponding maximal ergodic inequalities and individual ergodic theorems were derived. In this article, we derive maximal ergodic inequalities in noncommutative Lp-spaces directly from [25] and apply them to prove corresponding individual and Besicovitch weighted ergodic theorems. Then we extend these results to noncommutative fully symmetric Banach spaces with Fatou property and non-trivial Boyd indices, in particular, to noncommutative Lorentz spaces Lpq. Norm convergence of ergodic averages in noncommutative fully symmetric Banach spaces is also studied.

Related

• Noncommutative maximal ergodic theorems
• Individual ergodic theorems in noncommutative symmetric spaces
• Noncommutative ergodic averages of balls and spheres over Euclidean spaces
• On multiparameter Weighted ergodic theorem for Noncommutative L_p-spaces
• A noncommutative maximal inequality for ergodic averages along arithmetic sets