On some normality-like properties and Bishop's property (β) for a class of operators on Hilbert spaces

Abstract

We prove some further properties of the operator T ∈ [nQN] (n-power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator T ∈ [nQN] satisfying the translation invariant property is normal and that the operator T ∈ [nQN] is not supercyclic provided that it is not invertible. Also, we study some cases in which an operator T ∈ [2QN] is subscalar of order m; that is, it is similar to the restriction of a scalar operator of order m to an invariant subspace. Copyright © 2012 Sid Ahmed Ould Ahmed Mahmoud.