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N-SUPERCYCLICITY OF AN A-m-ISOMETRY

  • HEDAYATIAN, KARIM (Department of Mathematics, College of Sciences, Shiraz University)
  • Received : 2015.03.24
  • Accepted : 2015.05.06
  • Published : 2015.09.25

Abstract

An A-m-isometric operator is a bounded linear operator T on a Hilbert space $\mathcal{H}$ satisfying $\sum\limits_{k=0}^{m}(-1)^{m-k}T^{*^k}AT^k=0$, where A is a positive operator. We give sufficient conditions under which A-m-isometries are not N-supercyclic, for every $N{\geq}1$; that is, there is not a subspace E of dimension N such that its orbit under T is dense in $\mathcal{H}$.

Keywords

Hilbert space;A-m-isometry;N-supercyclicity

Acknowledgement

Supported by : Shiraz University

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