Relative position of four subspaces in a Hilbert space

Masatoshi Enomoto, Yasuo Watatani

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)263-317
Number of pages55
JournalAdvances in Mathematics
Volume201
Issue number2
DOIs
Publication statusPublished - Apr 1 2006

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Hilbert space
Subspace
Defects
Fredholm Index
Functor
Operator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Relative position of four subspaces in a Hilbert space. / Enomoto, Masatoshi; Watatani, Yasuo.

In: Advances in Mathematics, Vol. 201, No. 2, 01.04.2006, p. 263-317.

Research output: Contribution to journalArticle

Enomoto, Masatoshi ; Watatani, Yasuo. / Relative position of four subspaces in a Hilbert space. In: Advances in Mathematics. 2006 ; Vol. 201, No. 2. pp. 263-317.
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