On maps preserving the Jordan product of $C$-symmetric operators

Abstract

Given a conjugation C on a complex separable Hilbert space H, a bounded linear operator A acting on H is said to be C-symmetric if A = CA * C. In this paper, we provide a complete description to all those maps on the algebra of linear operators acting on a finite dimensional Hilbert space that preserve the Jordan product of C-symmetric operators, in both directions, for every conjugation C on H.