Noncommutative weighted individual ergodic theorems with continuous time

2018/09/06 by Chilin, Vladimir, Litvinov, Semyon
#46L52 #47A35 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1809.01788

Abstract

We show that ergodic flows in noncommutative fully symmetric spaces (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford-Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly. The corresponding local ergodic theorem is also discussed.

Related

• Besicovitch-weighted ergodic theorems with continuous time
• Individual ergodic theorems in noncommutative symmetric spaces
• Individual ergodic theorems for semifinite von Neumann algebras
• On individual ergodic theorems for semifinite von Neumann algebras
• Ergodic theorems in fully symmetric spaces of τ-measurable operators