论文标题
1型1型分子代数的最大和有限性
Maximality and finiteness of type 1 subdiagonal algebras
论文作者
论文摘要
让$ \ mathfrak a $为$σ$ -finite von neumann代数$ \ mathcal m $的1型子diagonal代数。我们提供了$ \ mathfrak $ $ \σ$ weakly封闭的$ \ mathcal m $的$σ$ weakly封闭的亚代词的必要条件。此外，我们还表明，有限的von Neumann代数中的1型子谱系代数是自动有限的，在1967年，在1型情况下，在1967年为Arveson的有限问题提供了正面答案。
Let $\mathfrak A$ be a type 1 subdiagonal algebra in a $σ$-finite von Neumann algebra $\mathcal M$ with respect to a faithful normal conditional expectation $Φ$. We give necessary and sufficient conditions for which $\mathfrak A$ is maximal among the $σ$-weakly closed subalgebras of $\mathcal M$. In addition, we show that a type 1 subdiagonal algebra in a finite von Neumann algebra is automatically finite which gives a positive answer of Arveson's finiteness problem in 1967 in type 1 case.
