Relative position of four subspaces in a Hilbert space

Details Relative position of four subspaces in a Hilbert space Relative position of four subspaces in a Hilbert space

2004-04-30

arxiv.org/abs/math/0404545v2

Mathematics

Operator Algebras

48 pages,improved content for section 12

Scientific paper

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.

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