Abstract
Let X and Y be two in finite-dimensional complex Banach spaces, and fix two nonzero vectors x(0) is an element of X and y(0) is an element of Y. Let B(X) (resp. B(Y)) denote the algebra of all bounded linear operators on X (resp. on Y). We show that a map phi from B(X) onto B(Y) satisfies
sigma(phi(T)phi(S)+phi(S)phi(T))(y(0)) = sigma(TS + ST)(x(0)) (T, S is an element of B(X))
if and only if there exists a bijective bounded linear mapping A from X into Y such that Ax(0) = y(0) and either phi(T) = ATA(-1) for all T is an element of B(X) or phi(T) = -ATA(-1) for all T is an element of B(X).