Relative position of four subspaces in a Hilbert space

Masatoshi Enomoto, Yasuo Watatani

    Research output: Contribution to journalArticlepeer-review

    14 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

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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