Resumen de Characterizations of Lie-skew multiplicative maps on operator algebras of indefinite inner product spaces

Runling An, Jinchuan Hou

• Let H and K be inde¯nite inner product spaces. In this paper, we show that a bijective map © : B(H) ! B(K) satis¯es ©(AB ¡ BAy) = ©(A)©(B) ¡ ©(B)©(A)y for every pair A;B 2 B(H) if and only if there exist a unitary or conjugate unitary operator U 2 B(H;K) such that ©(A) = UAU y for all A 2 B(H).