We show that ergodic flows in the noncommutative [Formula: see text]-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 [Formula: see text]-spaces), Lorentz, and Marcinkiewicz spaces. The commutative counterparts of the results are derived.

中文翻译：

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具有连续时间的非对易加权个体遍历定理

我们证明了由正 Dunford-Schwartz 算子的连续半群生成并由有界 Besicovitch 几乎周期函数调制的非交换 [公式：见文本]-空间（与半有限冯诺依曼代数相关）中的遍历流几乎均匀地收敛。相应的局部遍历定理也得到了证明。然后，我们将这些结果扩展到任意非交换完全对称空间，并将其应用于非交换 Orlicz（特别是非交换 [公式：见文本]-空间）、Lorentz 和 Marcinkiewicz 空间。推导出结果的可交换对应物。