Abstract.
We study the relative position of four (closed) subspaces in a Hilbert space. For any positive integer n, we give an example of exotic indecomposable system \({\mathcal{S}}\) of four subspaces in a Hilbert space whose defect is \(\frac{2n+1}{3}\). By an exotic system, we mean a system which is not isomorphic to any closed operator system under any permutation of subspaces. We construct the examples using certain nice sequences construced by Jiang and Wang in their study of strongly irreducible operators.
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Dedicated to Professor Masahiro Nakamura on his 88th birthday
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Enomoto, M., Watatani, Y. Exotic Indecomposable Systems of Four Subspaces in a Hilbert Space. Integr. equ. oper. theory 59, 149–164 (2007). https://doi.org/10.1007/s00020-007-1512-2
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DOI: https://doi.org/10.1007/s00020-007-1512-2