发表机构
IIT Guwahati（印度理工学院古瓦哈提分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在半有限冯·诺依曼代数上，通过引入$p$-凸Orlicz函数条件，建立了带算子值权重的调制$(C,\alpha)$平均的极大遍历定理与逐点收敛，并推广了Rota定理。
AI 中文摘要
本文在半有限冯·诺依曼代数框架下，研究了带算子值权重的调制$(C,\alpha)$遍历平均及其子序列版本。我们的框架结合了$(C,\alpha)$型调制与算子值权重，并推广了标量权重和算子值权重的遍历理论。我们在非交换$L_p$空间上建立了这些平均的均值遍历定理和极大不等式。随后，我们研究了非交换Orlicz空间中的双边几乎一致收敛和几乎一致收敛，包括沿密度为一的子序列的收敛。我们方法的一个关键要素是对底层Orlicz函数引入$p$-凸性条件。该条件使我们能够从非交换$L_p$空间转移适当的极大估计，以在相应的非交换$p$-凸Orlicz空间上建立零处测度意义下的双边一致等度连续性。结合非交换Banach原理，这产生了所需的逐点收敛结果。作为我们$p$-凸性论证的额外推论，我们将Rota定理推广到与本文所考虑的$p$-凸Orlicz函数相关的更大一类非交换Orlicz空间。
英文摘要
In this paper, we study modulated $(C,α)$-ergodic averages with operator-valued weights and their subsequential versions in the setting of semifinite von Neumann algebras. Our framework combines $(C,α)$-type modulation with operator-valued weights and extends both scalar-weighted and operator-valued weighted ergodic theories. We establish mean ergodic theorems and maximal inequalities for these averages on noncommutative $L_p$-spaces. We then study bilateral almost uniform and almost uniform convergence in noncommutative Orlicz spaces, including convergence along subsequences of density one. A key ingredient in our approach is the introduction of the $p$-convexity condition on the underlying Orlicz function. This condition enables us to transfer appropriate maximal estimates from noncommutative $L_p$-spaces to establish bilateral uniform equicontinuity in measure at zero on the corresponding noncommutative $p$-convex Orlicz spaces. Together with the noncommutative Banach principle, this yields the desired pointwise convergence results. As an additional consequence of our $p$-convexity argument, we extend Rota's theorem to a larger class of noncommutative Orlicz spaces associated with the $p$-convex Orlicz functions considered in this article.
CommentsPreliminary Version, Comments are welcome
