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 ϕ \phi of a certain abstract complete lattice P P (defined by N. Zierler) there exists an element a ∈ P a \in P different from 0 and 1 such that ϕ 2 ( a ) ≤ a {\phi ^2}(a) \leq a .
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