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arXiv · 1908.01935

On the non-hypercyclicity of normal operators, collections of their exponentials, and symmetric operators

Marat V. Markin·Edward S. Sichel
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Abstract

We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary normal operator $A$ (bounded or unbounded) in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which, under a certain condition on the spectrum of $A$, is the $C_0$-semigroup generated by it. We also establish non-hypercyclicity for symmetric operators.

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Marat V. Markin, Edward S. Sichel. 2019-08-06. On the non-hypercyclicity of normal operators, collections of their exponentials, and symmetric operators. https://arxiv.org/abs/1908.01935

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