A lattice-theoretic equivalent of the invariant subspace problem

Longstaff, W. E.

doi:10.1090/S0002-9939-1986-0861759-5

A lattice-theoretic equivalent of the invariant subspace problem
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Proc. Amer. Math. Soc. 98 (1986), 605-606 Request permission

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 ${\phi ^2}(a) \leq a$.

References

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