Mathematics Department, College of Science, Al Jouf University, Al Jouf 2014, Saudi Arabia
Copyright © 2012 Sid Ahmed Ould Ahmed Mahmoud. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.