An extension of Fourier-Stieltjes algebras on locally compact groups.
by
Ghorban Ali Bagheri-Bardi
Reasearcher In Gulf Persin University

Let \G and \GG be locally compact groups. The bi-Fourier-Stieltjes algebra B²(\G×\GG) is the space of all bi-coefficients of unitary representations of \G and \GG: the map f:\G×\GG→ C is in B²(\G×\GG) if there are unitary representations p_i:G_i\ToB(H_i) and a bounded operator T:\h₂→\h₁ such that

f(s, t)= < p1(s) Tp2(t)h|z >

where h ∈ \hh and z ∈ \h₁. We prove the bi-Fourier-Stieltjes algebra B²(\G×\GG) is a completely contractive commutative Banach algebra under the pointwise multiplication. We show it contains a copy of the Fourier-Stieltjes algebra B(\G×\GG) and then extends some classical results on B²(\G×\GG).

Date received: January 16, 2010