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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bès, J. Martin, Ö. Peris, A. and Shkarin, S. 2012. Disjoint mixing operators. Journal of Functional Analysis, Vol. 263, Issue. 5, p. 1283.

    Rodríguez-Martínez, Alejandro 2012. Residuality of Sets of Hypercyclic Operators. Integral Equations and Operator Theory, Vol. 72, Issue. 3, p. 301.

    Salas, Héctor N. 2011. Dual disjoint hypercyclic operators. Journal of Mathematical Analysis and Applications, Vol. 374, Issue. 1, p. 106.

    Shkarin, Stanislav 2010. A short proof of existence of disjoint hypercyclic operators. Journal of Mathematical Analysis and Applications, Vol. 367, Issue. 2, p. 713.



  • HÉCTOR N. SALAS (a1)
  • DOI:
  • Published online: 01 May 2007

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.

5.L. Bernal-González , On hypercyclic operators on Banach spaces, Proc. Amer. Math. Soc. 127 (1999), no. 4, 10031010.

6.J. P. Bès and A. Peris , Hereditarily hypercyclic operators, J. Funct. Anal. 167 (1999), no. 1, 94112.

7.J. Bonet and A. Peris , Hypercyclic operators on non-normable Fréchet spaces, J. Funct. Anal. 159 (1998), no. 2, 587595.

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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