On skew C1C2-Symmetric operators

Abstract

                  Let C₁ and C₂ be conjugation operators, both of which are antilinear, isometric, and involution mappings, defined on a separable complex Hilbert space . This paper  introduces the concept of skew -symmetric operators ( -S.O). A bounded linear operator A  on  is classified as a  -S.O.  if it satisfies the condition ( C₁A = -A^⁕ C₂ ), or equivalently, ( A = -C₁ A* C₂ ). We examine and analyze several fundamental properties of such operators and provide a concrete example to illustrate this notion.