• Title/Summary/Keyword: supercyclic operators

Search Result 2, Processing Time 0.092 seconds

SUPERCYCLICITY OF TWO-ISOMETRIES

  • Ahmadi, M. Faghih;Hedayatian, K.
    • Honam Mathematical Journal
    • /
    • v.30 no.1
    • /
    • pp.115-118
    • /
    • 2008
  • A bounded linear operator T on a complex separable Hilbert space H is called a two-isometry, if $T^{*2}T^2-2T^*T+1=0$. In this paper it is shown that every two-isometry is not supercyclic. This generalizes a result due to Ansari and Bourdon.

Supercyclicity of Convex Operators

  • Hedayatian, Karim;Karimi, Lotfollah
    • Kyungpook Mathematical Journal
    • /
    • v.58 no.1
    • /
    • pp.81-90
    • /
    • 2018
  • 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.