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 Phi : B(H) -> B(K) satisfies Phi(AB(dagger) + B(dagger)A) = Phi(A)Phi(B)(dagger) + Phi(B)(dagger) + Phi(A) for every pair A, B is an element of B(H) if and only if either Phi(A) = cUAU(dagger) for all A or Phi(A) = cUA(dagger)U(dagger) for all A; Phi satisfies Phi(AB(dagger)A) = Phi(A)Phi(B)(dagger)Phi(A) for every pair A, B is an element of B(H) if and only if either Phi(A) = UAV for all A or Phi(A) = UA(dagger)V for all A, where A(dagger) denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with (UU)-U-dagger = c(-1) and (VV)-V-dagger = cI for some nonzero real number c.