Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Existence and nonexistence of hypercyclic semigroups

Author(s): L. Bernal-González; K.-G. Grosse-Erdmann
Journal: Proc. Amer. Math. Soc. 135 (2007), 755-766.
MSC (2000): Primary 47A16; Secondary 47D03
Posted: August 31, 2006
MathSciNet review: 2262871
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinite-dimensional Banach space that is very different from--and considerably shorter than--the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite-dimensional Fréchet space. This complements recent results due to Bès and Chan. Moreover, we discuss the Hypercyclicity Criterion for semigroups and we give an example of a separable infinite-dimensional locally convex space which supports no supercyclic strongly continuous semigroup of operators.

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