摘要
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(B)+ + Φ(B)+Φ(A) for every pair A,B ∈ B(H) if and only if either Φ(A) = cUAU+ for all A or Φ(A) = cUA+U+ for all A; Φ satisfies 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.
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(B)^+ + φ(B)^+φ(A) for every pair A, B ∈ B(H) if and only if either φ(A) = cUAU^+ for all A or φ(A) = cUA^+U^+ for all A; φ satisfies 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 At denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U^tU = c^-1I and V^+V = cI for some nonzero real number c.
基金
Project supported by the National Natural Science Foundation of China (No.10471082) the Shanxi Provincial Natural Science Foundation of China (No.20021005).