Decomposability and Norm Convergence Properties in Finite von Neumann Algebras
Decomposability and Norm Convergence Properties in Finite von Neumann Algebras
复制标题
有限冯诺依曼代数中的可分解性和范数收敛性
DOI：
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发表时间：
2018
影响因子：
0.8
通讯作者：
D. Zanin
中科院分区：
文献类型：
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作者：
K. Dykema;J. Noles;D. Zanin
我们研究了具有忠实、正规、迹状态的冯诺依曼代数元素T的舒尔型上三角形式。这些都是在一份文件中介绍了Dykema，Sukochev和Zanin;他们是基于Haagerup-Schultz预测。我们调查了特别行动小组- T的分解的拟幂零部分实际上是拟幂零的。证明了T的可分解性和强可分解性。我们证明了这与序列的范数收敛性质有关|T^n|联系我们|TN| 1/n，由Haagerup和Schultz的结果，已知收敛于强算子拓扑。我们引入了Borel可分解性，这是一个适合于有限冯诺依曼代数元素的属性，并证明了循环算子是Borel可分解的。我们还证明了存在一个薄谱s. o.t. -超有限II$1$$1-因子中的拟幂零算子。
We study Schur-type upper triangular forms for elements, T, of von Neumann algebras equipped with faithful, normal, tracial states. These were introduced in a paper of Dykema, Sukochev and Zanin; they are based on Haagerup–Schultz projections. We investigate when the s.o.t.-quasinilpotent part of this decomposition of T is actually quasinilpotent. We prove implications involving decomposability and strong decomposability of T. We show this is related to norm convergence properties of the sequence $$|T^n|^{1/n}$$|Tn|1/n which, by a result of Haagerup and Schultz, is known to converge in strong operator topology. We introduce a Borel decomposability, which is a property appropriate for elements of finite von Neumann algebras, and show that the circular operator is Borel decomposable. We also prove the existence of a thin-spectrum s.o.t.-quasinilpotent operator in the hyperfinite II$$_1$$1-factor.