关于可测算子列的一致等度连续性
On Uniform Equicontinuity of Sequences of Measurable Operators
摘要：
讨论了半有限vonNeumann代数上从赋范空间到可测算子空间的可加映射序列在零测度上一致等度连续的概念。证明了稠密子集上在零点处按测度一致等度连续蕴涵了整个空间上的一致等度连续，并利用这一结果导出了一些非交换的遍历定理
英文摘要：
The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform equicontinuity in measure at zero on a dense subset implies the uniform equicontinuity on the entire space, which is then applied to derive some non-commutative ergodic theorems
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