On n-binormal Operators

In this paper we introduce n-binormal operators acting on a Hilbert space H. An operator T ∈ L(H ) is n-binormal if n T^* T^n commutes with T^* T^n or [ T^* T^n, T^n T^*]=0 and it is denoted by [nBN]. We investigate some basic properties of such operators. In general a n-binormal operator need not be a normal operator. Further we study n-binormal composite integral operators.