Abstract
Let B(H) denote the algebra of all bounded linear operators acting on a complex Hilbert space H. In this paper, we show that a surjective map phi on B(H) satisfies
sigma(phi(T)phi(S) - phi(S)phi(T)*) = sigma(TS - ST*), T, S is an element of B(H),
if and only if there exists a unitary operator U is an element of B(H) such that
phi(T) = lambda UTU*, T is an element of B(H),
where lambda is an element of {-1, 1}.