Integral Equations and Operator Theory

, Volume 64, Issue 4, pp 487–494 | Cite as

On the Orbit of an m-Isometry

  • Teresa Bermúdez
  • Isabel Marrero
  • Antonio Martinón
Article

Abstract.

A bounded linear operator T on a Hilbert space H is called an m-isometry for a positive integer m if \(\sum\nolimits_{{k = 0}}^{m} {( - 1)^{{m - k}} } \left( {\begin{array}{*{20}c} m \\ k\\ \end{array} } \right)T^{{*k}} T^{k} = 0\). We prove some properties concerning the behaviour of the orbit of an m-isometry. For example, every orbit of an m-isometry is eventually norm increasing and some m-isometries can not be N-supercyclic, that is, there does not exist an N-dimensional subspace EN such that the orbit of T at EN is dense in H.

Mathematics Subject Classification (2000).

47A16 

Keywords.

Isometry m-isometry supercyclic N-supercyclic 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Teresa Bermúdez
    • 1
  • Isabel Marrero
    • 1
  • Antonio Martinón
    • 1
  1. 1.Departamento de Análisis MatemáticoUniversidad de La LagunaLa LagunaSpain

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