The invariant subspace structure of nonselfadjoint crossed products
The invariant subspace structure of nonselfadjoint crossed products
复制标题
非自共叉积的不变子空间结构
DOI：
10.1090/s0002-9947-1983-0709586-5
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
B. Solel
中科院分区：
文献类型：
--
作者：
B. Solel
设£是由有限的冯·诺伊曼代数M和M的保迹自同构a决定的冯·诺伊曼代数的交叉积。我们研究了由在£上的对偶自同构群上谱为非负的算子组成的子代数£+的不变子空间结构。我们研究了在£'中对于部分等距R0，两个不变子空间911和9H2满足Qt - RVQ2R*V的条件（qq2为相应的正交投影）。利用这一分析，我们找到了包含£+的£的o弱闭子代数的一般形式。
Let £ be the von Neumann algebra crossed product determined by a finite von Neumann algebra M and a trace preserving '-automorphism a of M. We study the invariant subspace structure of the subalgebra £+ of £ consisting of those operators whose spectrum with respect to the dual automorphism group on £ is nonnegative. We investigate the conditions for two invariant subspaces 911, and 9H2 (with Qu Q2 the corresponding orthogonal projections) to satisfy Qt — RVQ2R*V for some partial isometry R0 in £'. We use this analysis to find the general form of a o-weakly closed subalgebra of £ that contains £+ .