On the Non-Hypercyclicity of Normal Operators, Their Exponentials, and Symmetric Operators

Marat V. Markin and Edward S. Sichel
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Marat V. Markin: Department of Mathematics, California State University, Fresno, 5245 N. Backer Avenue, M/S PB 108, Fresno, CA 93740-8001, USA
Edward S. Sichel: Department of Mathematics, California State University, Fresno, 5245 N. Backer Avenue, M/S PB 108, Fresno, CA 93740-8001, USA

Mathematics, 2019, vol. 7, issue 10, 1-8

Abstract: We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator A in a complex Hilbert space as well as of the collection e t A t ≥ 0 of its exponentials, which, under a certain condition on the spectrum of A , coincides with the C 0 -semigroup generated by it. We also establish non-hypercyclicity for symmetric operators.

Keywords: hypercyclicity; scalar type spectral operator; normal operator; C 0 -semigroup (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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