Weak Haagerup property of dynamical systems

Using Herz-Schur multipliers of a C*-dynamical system, we introduce the weak Haagerup property of a C*-dynamical system and prove that it is equivalent to the weak Haagerup property of the associated C*-crossed product. On the other hand, we investigate an additional assumption under which the weak Haagerup property of the original C*-algebra and the group implies that of the associated C*-dynamical system. We also define and study the weak Haagerup property of a W*-dynamical system.