### 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 II_{1} factor setting.

Original language | English |
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Pages (from-to) | 263-317 |

Number of pages | 55 |

Journal | Advances in Mathematics |

Volume | 201 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 1 2006 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Enomoto, M., & Watatani, Y. (2006). Relative position of four subspaces in a Hilbert space.

*Advances in Mathematics*,*201*(2), 263-317. https://doi.org/10.1016/j.aim.2005.02.004