Quasi Triple Operator of Order

In this study, two new classes of operators on a complex Hilbert space H were presented and referred to as the Quasi-triple operator and quasi-triple operator. Quasi-triple operator is denoted as qt-operator, and the quasi-triple operator is denoted as qt-operator where  is a linear bounded operator on H. The generalization of the above concepts is Quasi-triple operator of order n and quasi-triple operator of order n. Some results of these two types of operators including sum, product, direct sum and tensor product operations have been discussed. We also presented some results and theorems and supported the discussion with some illustrative examples.