Order Structure of the Figà-Talamanca-Herz Algebra

Abstract EN

We study the interplay between the order structure and the p-operator space structure of Figà-Talamanca-Herz algebra Ap(G) of a locally compact group G.

We show that for amenable groups, an order and algebra isomorphism of Figà-Talamanca-Herz-algebras yields an isomorphism or anti-isomorphism of the underlying groups.

We also give a bound for the norm of a p-completely positive linear map from Figà-Talamanca-Herz algebra to its dual space.