CHARACTERIZATIONS OF JORDAN (?)-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES

Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ:B(H)→B(K) satisfies φ(AB+ + B+A) =φ(A)φ(5)+ +φ(B)+φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = cU AU+ for all A or φ(A) = cUA+U+ for all A; φsatisfies φ(AB+A) = φ(A)φ(B)+φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = UAV for all A or φ(A) = UA+V for all A, where A+ denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U+U = c-1I and V+V = cI for some nonzero real number c.