Hypercyclic Operators That Commute with the Bergman Backward Shift
نویسنده
چکیده
The backward shift B on the Bergman space of the unit disc is known to be hypercyclic (meaning: it has a dense orbit). Here we ask: “Which operators that commute with B inherit its hypercyclicity?” We show that the problem reduces to the study of operators of the form φ(B) where φ is a holomorphic self-map of the unit disc that multiplies the Dirichlet space into itself, and that the question of hypercyclicity for such an operator depends on how freely φ(z) is allowed to approach the unit circle as |z| → 1−.
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