On crossed products and Takai duality

Abstract

The Takai duality theorem has proved to be a fundamental tool in the theory of crossed products of C *-algebras. It was inspired by Takesaki's duality theorem for crossed products of von Neumann algebras [ 7 ], so it is not surprising that the original proof [ 6 ] depended heavily on spatial techniques. Here we shall prove Takai's theorem by exploiting the universal properties of crossed products.