On Some Normality-Like Properties and Bishop's Property () for a Class of Operators on Hilbert Spaces

Abstract

We prove some further properties of the operator (-power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator satisfying the translation invariant property is normal and that the operator is not supercyclic provided that it is not invertible. Also, we study some cases in which an operator is subscalar of order ; that is, it is similar to the restriction of a scalar operator of order to an invariant subspace.