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Proceedings of the American Mathematical Society

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A lattice-theoretic equivalent of the invariant subspace problem


Author: W. E. Longstaff
Journal: Proc. Amer. Math. Soc. 98 (1986), 605-606
MSC: Primary 47A15; Secondary 06B99
DOI: https://doi.org/10.1090/S0002-9939-1986-0861759-5
MathSciNet review: 861759
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Abstract: Every bounded linear operator on complex infinite-dimensional separable Hilbert space has a proper invariant subspace if and only if for every lattice automorphism $ \phi $ of a certain abstract complete lattice $ P$ (defined by N. Zierler) there exists an element $ a \in P$ different from 0 and 1 such that $ {\phi ^2}(a) \leq a$.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0861759-5
Article copyright: © Copyright 1986 American Mathematical Society

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