Weak* continuous states on Banach algebras (Q2517688)

Let \(A\) be a dual Banach space. Given a norm-one element \(x \in A\), the set of states \(S^{x}(A)\) is defined to be the set of all elements \(\rho\) of the unit ball of the dual of \(A\) for which \(\rho(x) = 1.\) The set of normal states is then the subset obtained by intersecting \(S^{x}(A)\) with the predual of \(A\). It is proved that the set of normal states is weak*-dense in the set of all states of \(A.\)