Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Supercyclicity of Convex Operators

  • Hedayatian, Karim (Department of Mathematics, College of Sciences, Shiraz University) ;
  • Karimi, Lotfollah (Department of Mathematics, College of Sciences, Shiraz University)
  • Received : 2015.06.12
  • Accepted : 2017.12.06
  • Published : 2018.03.23
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Abstract

A bounded linear operator T on a Hilbert space ${\mathcal{H}}$ is convex, if for each $x{\in}{\mathcal{H}}$, ${\parallel}T^2x{\parallel}^2-2{\parallel}Tx{\parallel}^2+{\parallel}x{\parallel}^2{\geq}0$. In this paper, it is shown that if T is convex and supercyclic then it is a contraction or an expansion. We then present some examples of convex supercyclic operators. Also, it is proved that no convex composition operator induced by an automorphism of the disc on a weighted Hardy space is supercyclic.

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