Article
Existence and nonexistence of hypercyclic semigroups
Author/s | Bernal González, Luis
Grosse-Erdmann, Karl-Goswin |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2007-03 |
Deposit Date | 2019-06-19 |
Published in |
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Abstract | In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from –and considerably shorter
than– ... In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional 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. |
Project ID. | FQM-127
BFM2003-03893-C02-01 |
Citation | Bernal González, L. y Grosse-Erdmann, K. (2007). Existence and nonexistence of hypercyclic semigroups. Proceedings of the American Mathematical Society, 135 (3), 755-766. |
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