Geodesic
Existence of hypercyclic subspaces for Toeplitz operators
Ufa mathematical journal, Tome 7 (2015) no. 2, pp. 102-105

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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 $\mathbb D$ and continuous in its closure the conditions $\varphi(\mathbb T)\cap\mathbb T\ne\emptyset$ and $\varphi(\mathbb D)\cap\mathbb T\ne\emptyset$ 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.
Keywords: Toeplitz operators, hypercyclic operators, essential spectrum, Hardy space. 
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     title = {Existence of hypercyclic subspaces   for {Toeplitz} operators},
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A. A. Lishanskii. Existence of hypercyclic subspaces   for Toeplitz operators. Ufa mathematical journal, Tome 7 (2015) no. 2, pp. 102-105. http://geodesic.mathdoc.fr/item/UFA_2015_7_2_a6/