k-Jordan * maps on ℬ(ℋ).

Let ℬ(ℋ) be a algebra on complex number space C,k ∈ C is nonzero. Using some methods of operator theory, it is proved that, if ɸ : ℬ(ℋ) → ℬ(H) is a bijective map and satisfies ɸ(k(AB* + B* A)) = k(ɸ(A)ɸ(B)* + ɸ (B)* ɸ(A)) for every pair A, B ∈ ℬ(ℋ) if and only if ɸ is a * -isomorphism, or a *-anti-isomorphism; if ɸ is a bijective map and satisfies ɸ(AB* A) =ɸ(A)ɸ(B)*ɸ(A) for every pair A, B&#8712 ℬ(ℋ) if and only if ɸ is a * -isomorphism, or a conjugate * -isomorphism, or a * -anti-isomorphism, or a conjugate * -anti-isomorphism. [ABSTRACT FROM AUTHOR]