论文标题
关于半决赛von Neumann代数的单个千古定理
On individual ergodic theorems for semifinite von Neumann algebras
论文作者
论文摘要
众所周知，对于非交通性$ l^p $ - 空格的积极的邓福德·史加兹（Dunford-Schwartz）运营商，$ 1 \ leq p <\ infty $，或者更一般而言，在非订单持续规范的空间中，相应的Ergodic平均均衡器收敛于双层均匀均匀。我们表明，这些平均值几乎在每个非承认对称空间$ e $中均匀地汇合，因此每个$ t \ to $ t \ to $ t \ to \ t \ to \ infty $的每个$ x \ in e $中的$μ_t（x）$是$ x $ $ x $的不添加。研究了非共同的Dunford-Schwartz-type多参数ergodic定理。概述了Dunford-Schwartz型单个ergodic定理的广泛非交换对称空间。
It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p$-space, $1\leq p<\infty$, or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge bilaterally almost uniformly. We show that these averages converge almost uniformly in each noncommutative symmetric space $E$ such that $μ_t(x)\to 0$ as $t\to\infty$ for every $x\in E$, where $μ_t(x)$ is the non-increasing rearrangement of $x$. Noncommutative Dunford-Schwartz-type multiparameter ergodic theorems are studied. A wide range of noncommutative symmetric spaces for which Dunford-Schwartz-type individual ergodic theorems hold is outlined.
