Table of Contents
ISRN Geometry
Volume 2011, Article ID 531023, 13 pages
http://dx.doi.org/10.5402/2011/531023
Research Article

Order Structure of the Figà-Talamanca-Herz Algebra

1Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran
2Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran

Received 30 March 2011; Accepted 21 April 2011

Academic Editors: V. S. Matveev and E. Previato

Copyright © 2011 Marzieh Shams Yousefi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the interplay between the order structure and the 𝑝 -operator space structure of 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 Figà-Talamanca-Herz algebra to its dual space.