Order structure of the Figà-Talamanca-Herz algebra
Summary: We study the interplay between the order structure and the \(p\)-operator space structure of the Figà-Talamanca-Herz algebra \(A_p(G)\) 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 a Figà-Talamanca-Herz algebra to its dual space.
scientific article; zbMATH DE number 5931061
scientific article