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

DOI:
https://doi.org/10.1090/S0002-9939-1991-1049848-8

MathSciNet review:
1049848

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Abstract | References | Similar Articles | Additional Information

Abstract: An operator acting on a Hilbert space is hypercyclic if, for some vector in , the orbit is dense in . 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:
https://doi.org/10.1090/S0002-9939-1991-1049848-8

Keywords:
Cyclic vectors,
hypercyclic vectors and operators,
weighted shifts

Article copyright:
© Copyright 1991
American Mathematical Society