Noncommutative weighted individual ergodic theorems with continuous time. (English) Zbl 1520.47025
Summary: We show that ergodic flows in the noncommutative \(L^1\)-space (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 proved. We then extend these results to arbitrary noncommutative fully symmetric spaces and present applications to noncommutative Orlicz (in particular, noncommutative \(L^p\)-spaces), Lorentz, and Marcinkiewicz spaces. The commutative counterparts of the results are derived.
Keywords:
Dunford-Schwartz operator; continuous semigroup; bounded Besicovitch function; almost uniform convergenceReferences:
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