On metric equivalence of operators of order N

Abstract

Class of operators satisfying V*nVn= Q*nQn is introduced which is an equivalence relation, that is Metric equivalence of order n. We examine some properties that this class enjoys. On the same note, we study the relation of this class to other classes of operators like K* quasinormal operators of order n and normal of order n. We give a condition under which V*nVn= Q*nQn is same as V*Vn= Q*Qn and V*nVm= Q*nQm, that is n-power and (n,m)-power-Metric equivalences respectively.