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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A hypercyclic operator whose adjoint is also hypercyclic


Author: Héctor Salas
Journal: Proc. Amer. Math. Soc. 112 (1991), 765-770
MSC: Primary 47A65; Secondary 47B37
MathSciNet review: 1049848
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Abstract: An operator $ T$ acting on a Hilbert space $ H$ is hypercyclic if, for some vector $ x$ in $ H$, the orbit $ \{ {T^n}x:n \geq 0\} $ is dense in $ H$. We show the existence of a hypercyclic operator--in fact, a bilateral weighted shift--whose adjoint is also hypercyclic. This answers positively a question of D. A. Herrero.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1049848-8
PII: S 0002-9939(1991)1049848-8
Keywords: Cyclic vectors, hypercyclic vectors and operators, weighted shifts
Article copyright: © Copyright 1991 American Mathematical Society