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Hypercyclic composition operators on Hilbert spaces of analytic functions in a Banach space. (English) Zbl 1324.47017

A bounded operator \(T\) on a Hilbert space \(E\) is called hypercyclic if there exists a vector \(x\in E\) such that the set \(\{ T^n x: n\in \mathbb N\}\) is dense in \(E\). The authors find hypercyclicity conditions for composition operators on Hilbert spaces of analytic functions of infinitely many variables. They also construct examples of Hilbert spaces of analytic functions which do not admit hypercyclic operators of composition with linear operators.

MSC:

47A16 Cyclic vectors, hypercyclic and chaotic operators
47B33 Linear composition operators
46G20 Infinite-dimensional holomorphy
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