Triple Operators of Order n on a Hilbert Space

Abstract

In this paper, we introduce a new class of operators on a complex Hilbert space H which is called triple operators of order n. An operator T∈B(H) is called triple operator of order n if (T^n T^* )T=T(〖T^n T〗^* ) for all n≥2 . where T^* is the adjoint of the operator T.We investigate some basic properties of such operators and study the relation between the triple operators of order n and some kinds of operators.