NC-symmetric operators

Abstract

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.