On maps preserving C-symmetric triple Jordan product of pairs of operators

Abstract

A bounded linear operator T, which operates on a complex separable Hilbert space H, is referred to as C-symmetric if T = CT* C, where C represents a conjugate-linear isometric involution on H. In this paper, we thoroughly investigate mappings ?: B(H) ? B(H), where B(H) denotes the algebra of all bounded linear operators on H, that fulfill the following condition: ABA is C-symmetric ?? ?(A)?(B)?(A) is C-symmetric for all A, B ? B(H) and conjugations C on H.