Relative position of four subspaces in a Hilbert space |
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Authors: | Masatoshi Enomoto |
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Affiliation: | a College of Business Administration and Information Science, Koshien University, Takarazuka, Hyogo 665, Japan b Department of Mathematical Sciences, Kyushu University, Hakozaki, Fukuoka, 812-8581, Japan |
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Abstract: | 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 II1 factor setting. |
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Keywords: | 46C07 47A15 15A21 16G20 16G60 |
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