Relative position of four subspaces in a Hilbert space
Relative position of four subspaces in a Hilbert space
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DOI：
10.1016/j.aim.2005.02.004
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发表时间：
2004-04
影响因子：
1.7
通讯作者：
M. Enomoto;Y. Watatani
中科院分区：
文献类型：
--
作者：
M. Enomoto;Y. Watatani
研究了可分无限维Hilbert空间中几个子空间的相对位置。在有限维情形下，Gelfand和Ponomarev给出了四个子空间的不可分解系统的完全分类。我们在无限维Hilbert空间中构造了由四个子空间组成的不可分解系统的奇异例子。我们推广了他们的Coxeter函子，并利用Fredholm指标进行了亏损。子空间的相对位置与强不可约算子和传递格有着密切的联系。在II1型因素设置中，缺陷与琼斯指数之间存在关系。
We study the relative position of several subspaces in a separable infinite-dimensional Hilbert space. In finite-dimensional case, Gelfand and Ponomarev gave a complete classification of indecomposable systems of four subspaces. We construct exotic examples of indecomposable systems of four subspaces in infinite-dimensional Hilbert spaces. We extend their Coxeter functors and defect using Fredholm index. The relative position of subspaces has close connections with strongly irreducible operators and transitive lattices. There exists a relation between the defect and the Jones index in a type II1factor setting.