Some Properties of* - Quasihyponormal Operators

In this paper, we introduce a new generalization for hyponormal operator which is *- quasihyponormal and discussion some important theorems of this concept, as well as, some properties of this operator have been given following this work. Finally, this work given other objective is solvability of some types of bounded linear operator call - commuting operator equation when has *-quasihyponormal operator and fined the value of these equations in a Hilbert space H.