Article
Ufa Mathematical Journal
Volume 7, Number 2, pp. 102-105
Existence of hypercyclic subspaces for Toeplitz operators
Lishanskii A.A.
DOI:10.13108/2015-7-2-102
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In this work we construct a class of coanalytic Toeplitz operators, which have an infinite-dimensional closed subspace, where any non-zero vector is hypercyclic. Namely, if for a function $\varphi$ which is analytic in the open unit disc $\mathds{D}$ and continuous in its closure the conditions $\varphi(\mathds{T}) \cap \mathds{T} \ne \emptyset$ and $\varphi(\mathds{D}) \cap \mathds{T} \ne \emptyset$ are satisfied, then the operator $\varphi (S^*)$ (where $S^*$ is the backward shift operator in the Hardy space) has the required property. The proof is based on an application of a theorem by Gonzalez, Leon-Saavedra and Montes-Rodriguez.