Analytic Subalgebras of Von Neumann Algebras
Analytic Subalgebras of Von Neumann Algebras
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冯诺依曼代数的解析子代数
DOI：
10.4153/cjm-1987-005-4
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
K. Saito
中科院分区：
文献类型：
--
作者：
P. Muhly;K. Saito
设M是von Neumann代数，{α t } t ∈ R是M上的σ-弱连续流，即，设{α t } t <$R是M的 *-自同构的单参数群，使得对于M的预对偶M <$中的每个ρ和对于每个x <$M，t的函数ρ（α t（x））在R上连续。近年来，M的子空间H ∞（α）受到了广泛的关注，H∞（α）定义为：其中H ∞（R）是由上半平面上有界解析函数的边值组成的经典哈代空间。在[8]的定理3.15中，证明了H∞（α）是M的σ-弱闭子代数，其中含有单位算子使得在M中是σ-弱稠密的，并且使得
Let M be a von Neumann algebra and let {α t } t∊R be a σ-weakly continuous flow on M; i.e., suppose that {α t } t∊R is a one-parameter group of *-automorphisms of M such that for each ρ in the predual, M∗, of M and for each x ∊ M, the function of t, ρ(α t (x)), is continuous on R. In recent years, considerable attention has been focused on the subspace of M, H∞(α), which is defined to be where H ∞(R) is the classical Hardy space consisting of the boundary values of functions bounded analytic in the upper half-plane. In Theorem 3.15 of [8] it is proved that in fact H∞(α) is a σ-weakly closed subalgebra of M containing the identity operator such that is σ-weakly dense in M, and such that