On C₁C₂ symmetric operators

Abstract

Let C₁ and C₂ are conjugation operators (both are antiliner, isometric and invoulation) on a separable complex Hilbert space H. In this paper, we present the notion of C₁C₂- symmetric operators as: A bounded linear operator A on H is C₁C₂-symmetric operators if C₁A = A* C₂ (A = C₁ A*C₂). We study and discuss several properties and give an example for such kind of operators.

Subject Classification:

• Primary 30D55
• 47A15

Keywords:

• Conjugation operators
• C-symmetric operators
• C₁C₂-symmertic operators