Some results on C-normal operators

Abstract

A bounded linear operator on a complex Hilbert space ℋ is a C-normal operator if there exists a conjugation C on ℋ such that CT* TC=TT* . This class of operators seems a natural generalization of C-symmetric operators on a Hilbert space. In this paper, several results related to such a family are established. Then, we give sufficient conditions under which the product and sum of two C-normal operators is C-normal. Moreover, we investigate properties of tensor products of these operators. Some more associated for this class of operators are obtained.

Keywords

• c -symmetric
• c-skew-symmetric
• c-normal
• conjugation