INEQUALITIES OF OPERATOR POWERS

  • Lee, Eun-Young (Department of Mathematics, Kyungpook National University) ;
  • Lee, Mi-Ryeong (Faculty of Liberal Education, Kyungpook National University) ;
  • Park, Hae-Yung (Department of Mathematics, Kyungpook National University)
  • Published : 2008.03.25

Abstract

Duggal-Jeon-Kubrusly([2]) introduced Hilbert space operator T satisfying property ${\mid}T{\mid}^2{\leq}{\mid}T^2{\mid}$, where ${\mid}T{\mid}=(T^*T)^{1/2}$. In this paper we extend this property to general version, namely property B(n). In addition, we construct examples which distinguish the classes of operators with property B(n) for each $n{\in}\mathbb{N}$.