Complex C1C2 symmetric and finite rank operators

Abstract

An operator A in B(H) is called complex C1C2-symmetric if E two antilinear, isometric and involution C1, C2 such that C1A = A* C2 (A=C1A*C2). In this paper, we shows that when the rank one operator become C1C2-symmetirc operators. Moreover, we show that the compact operator is C1C2 -symmetric operator. Also, we award some examples of C1C2-symmetric operators.