No abstract

In this paper, we give some new properties of C1C2-symmetric operators and discuss some results about these kind of operators. Also, we describe the conditions that a binormal operator becomes normal operator and give necessary and sufficient conditions that C1C2- symmetric operators becomes a binormal operator. Finally, we solve the problem that a binormal operator is not closed under addition.

In this paper, we present a concept of nC- symmetric operator as  follows: Let A be a bounded linear operator on separable complex Hilbert space , the operator A is said to be nC-symmetric if there exists a positive number n (n  such that CAn = A*ⁿ C (An = C A*ⁿ C). We provide an example and study the basic properties of this class of operators. Finally, we attempt to describe the relation between nC-symmetric operator and some other operators such as Fredholm and self-adjoint operators.