2004/04/30 by Masatoshi Enomoto, Enomoto, Masatoshi, Yasuo Watatani +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #math.FA #math.OA #msc:16G60 #msc:46C07 #msc:47A15
paper · pdf · doi:10.48550/arxiv.math/0404545
48 pages,improved content for section 12
arxiv created 2004/08/16 · arxiv updated 2009/12/01
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.