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RELATIVE POSITION OF FOUR SUBSPACES IN A HILBERT SPACE

Authors
  • Enomoto, Masatoshi
  • 榎本, 雅俊
  • Watatani, Yasuo
  • 綿谷, 安男
Publication Date
Jan 01, 2004
Source
Kyushu University Institutional Repository (QIR)
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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 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.

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