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Pathological hypercyclic operators

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Abstract.

We exhibit a hypercyclic operator whose square is not hypercyclic. Our operator is necessarily unbounded since a result of S. Ansari asserts that powers of a hypercyclic bounded operator are also hypercyclic. We also exhibit an unbounded Hilbert space operator whose non-zero vectors are hypercyclic.

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Authors and Affiliations

  1. Department of Mathematics, University of Puerto Rico, Mayagüez, 00681, Puerto Rico

    Héctor N. Salas

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  1. Héctor N. Salas
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Correspondence to Héctor N. Salas.

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Received: 19 March 2005; revised: 18 July 2005

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Salas, H.N. Pathological hypercyclic operators. Arch. Math. 86, 241–250 (2006). https://doi.org/10.1007/s00013-005-1511-y

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  • DOI: https://doi.org/10.1007/s00013-005-1511-y

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