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Hypercyclicity for the Elements of the Commutant of an Operator

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Abstract

Given a bounded linear operator T acting on a complex Banach space, we obtain a spectral condition implying that each operator in the commutant of T different from λI has a hypercyclic multiple, and we show several examples of operators satisfying this condition. We emphasize that for some of these examples we do not have a description of the commutant of T.

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Authors and Affiliations

  1. Department of Mathematics Facultad de Ciencias, University of Cantabria, Avda. de los Castros s/n, 39071, Santander, Spain

    Manuel González

  2. Department of Mathematics, University of Cádiz, Avda. de la Universidad s/n, 11405, Jerez de la Frontera, Spain

    Fernando León-Saavedra

Authors
  1. Manuel González
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  2. Fernando León-Saavedra
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Corresponding author

Correspondence to Fernando León-Saavedra.

Additional information

The first author was supported by the Kingdom of Spain, Grant MTM2010-20190. The second author was supported by Junta de Andalucía FQM-257 and Vicerrectorado de investigación UCA.

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González, M., León-Saavedra, F. Hypercyclicity for the Elements of the Commutant of an Operator. Integr. Equ. Oper. Theory 80, 265–274 (2014). https://doi.org/10.1007/s00020-014-2129-x

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  • DOI: https://doi.org/10.1007/s00020-014-2129-x

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