Relative position of four subspaces in a Hilbert space
Abstract
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 infinitedimensional Hilbert space is also rich. In finitedimensonal 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 infinitedimensional Hilbert spaces. We extend their Coxeter functors and defect using Fredholm index. There exist close connections with strongly irreducible operators and transitive lattices.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:math/0404545
 Bibcode:
 2004math......4545E
 Keywords:

 Operator Algebras;
 Functional Analysis;
 46C07 (Primary) 47A15;
 16G60 (Secondary)
 EPrint:
 48 pages,improved content for section 12