Abstract
This paper is devoted to the problem of the existence of invariant subspaces for Toeplitz operators. Let Γ be a Lipschitzian arc in the plane and let f be a non-constant continuous functions on the unit circumference. It is proved that if there exists an open circle such that and if the modulus of continuity ωf of the function f satisfies the condition then the Toeplitz operator Tf in the Hardy space H2 has a nontrivial hyperinvariant subspace. For the proof of this theorem one makes use of the Lyubich-Matsaev theorem.
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