The Weak Banach-Saks Property in C*-Algebras

We show that a C*-algebra A has the weak Banach-Saks property if and only if it is type I and the kth-derivative of its spectrum  is empty for some k. It is equivalent to the existence of a finite chain J1 ⊂ J2 ⊂ … ⊂ J<n ⊂ A of closed ideals such that J1, J2/J1, …, A/Jn are all dual C*-algebras.