C*-crossed products of C*-algebras with the weak Banach-Saks property

Let (A, G, alpha) be a C*-dynamical system. In Section 2, we first treat the discrete group action case. We suppose that G acts freely on the spectrum of A. Then it is shown that A has the weak Banach-Saks property, if and only if G is discrete and the C*-crossed product A x (alpha) G has the weak Banach-Saks property. In Section 3, we shall consider the compact group action case. Let G be a compact group and consider the following conditions (1)-(3): (1) A has the weak Banach-Saks property; (2) A x. G has the weak Banach-Saks property; (3) the fixed point algebra A(alpha) of A has the weak Banach-Saks property. Then it is shown that we have (1) double right arrow (2) double right arrow (3). Furthermore we suppose that G is (compact) abelian. Then it is shown that the implication (3) double right arrow (2) holds, and that if A is of type I and if alpha is pointwise unitary, the implication (2) double right arrow (1) holds.