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BANACH SPACES WITH SEPARABLE DUALS SUPPORT DUAL HYPERCYCLIC OPERATORS

  • HÉCTOR N. SALAS (a1)
Abstract
Abstract

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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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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

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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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