TY - JOUR

T1 - Relative position of four subspaces in a Hilbert space

AU - Enomoto, Masatoshi

AU - Watatani, Yasuo

N1 - Funding Information:
The authors would like to thank the referee for his valuable comments, which improve the paper to be more readable. The authors are supported by the Grant-in-Aid for Scientific Research of JSPS.

PY - 2006/4/1

Y1 - 2006/4/1

N2 - 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 II1 factor setting.

AB - 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 II1 factor setting.

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U2 - 10.1016/j.aim.2005.02.004

DO - 10.1016/j.aim.2005.02.004

M3 - Article

AN - SCOPUS:33644869269

VL - 201

SP - 263

EP - 317

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -