Invariant subspaces and cocycles in nonselfadjoint crossed products
Invariant subspaces and cocycles in nonselfadjoint crossed products
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非自共轭交叉积中的不变子空间和余循环
DOI：
10.1016/0022-1236(82)90017-9
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发表时间：
1982
影响因子：
1.7
通讯作者：
K. Saito
中科院分区：
文献类型：
--
作者：
K. Saito
设G是紧交换群，其阿基米德全序对偶为Γ，L是由有限vonNeumann代数M和M的保迹自同构的单参数群{α γ} γ <$Γ确定的vonNeumann代数交叉积.本文研究了L的子代数L+的不变子空间和上圈的结构，这些子代数由关于L上对偶自同构群{β g} g <$G的谱非负的算子组成.我们的主要结果是：若M是因子，则L+是L的σ-弱闭子代数中的极大子代数.
Let G be a compact abelian group with the archimedean totally ordered dual Γ and let L be the von Neumann algebra crossed product determined by a finite von Neumann algebra M and a one-parameter group {α γ} γϵΓ of trace preserving∗-automorphisms of M. In this paper, we investigate the structure of invariant subspaces and cocycles for the subalgebra L+ of L consisting of those operators whose spectrum with respect to the dual automorphism group {β g} gϵG on L is nonnegative. Our main result asserts that if M is a factor, then L+ is maximal among the σ-weakly closed subalgebras of L.