Relative position of four subspaces in a Hilbert space

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The relative position of one subfactor of a factor has been proved quite rich since the work of Jones. We shall show that the theory of relative position of several subspaces of a separable infinite-dimensional Hilbert space is also rich. In finite-dimensonal 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. There exist close connections with strongly irreducible operators and transitive lattices.
48 pages,improved content for section 12

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Operator Algebras, Functional Analysis, 46C07 (Primary) 47A15, 16G60 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/71014

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0404545
 http://arxiv.org/abs/math/0404545

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arXiv