IUMJ

Title: On idempotents of completely bounded multipliers of the Fourier algebra $A(G)$

Authors: Ana-Maria Popa Stan

Issue: Volume 58 (2009), Issue 2, 523-536

Abstract:

Let $A(G)$ be the Fourier algebra of a locally compact group $G$ and $M_{cb}A(G)$ be the space of completely bounded multipliers of $A(G)$. We give a description of idempotents of $M_{cb}A(G)$ of norm one and then present a necessary condition for an idempotent to be in $M_{cb}A(G)$. In the last part of the paper, we discuss a class of free sets, called L-sets, whose characteristic function is an idempotent of $M_{cb}A(G)$, but not of $B(G)$.