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  • HÉCTOR N. SALAS (a1)

Let E be a Banach space such that its dual E* is separable. We show that there exists a hypercyclic bounded operator T on E such that its adjoint T* is also hypercyclic on E*. We also exhibit a new kind of dual hypercyclic operator. Thus answers affirmatively two of the questions raised by Henrik Petersson in a recent paper.

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1. E. Abakumov and J. Gordon , Common hypercyclic vectors for multiples of backward shift, J. Funct. Anal. 200 (2003), no. 2, 494504.

2. S. I. Ansari , Existence of hypercyclic operators on topological vector spaces, J. Funct. Anal. 148 (1997), no. 2, 384390.

4. F. Bayart , Common hypercyclic subspaces, Integral Equations and Operator Theory 53 (2005), no. 4, 467476.

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8. G. Godefroy and J. H. Shapiro , Operators with dense, invariant, cyclic vector manifolds J. Funct. Anal. 98 (1991), 229269.

11. K. G. Grosse-Erdman , Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 3, 345381.

12. F. León-Saavedra and A. Montes-Rodríguez , Linear structure of hypercyclic vectors, J. Funct. Anal. 148 (1997), no. 2, 524545.

14. D. A. Herrero , Limits of hypercyclic and supercyclic operators, J. Funct. Anal. 99 (1991), 179190.

15. H. Petersson , Spaces that admit hypercyclic operators with hypercyclic adjoints, Proc. Amer. Math. Soc. 134 (2005), 16711676.

17. H. N. Salas , A hypercyclic operator whose adjoint is also hypercyclic, Proc. Amer. Math. Soc. 112 (1991), no. 3, 765770.

18. H. N. Salas , Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), no. 3, 9931004.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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