علی باقری بردی

Let $\G$ and $\GG$ be locally compact groups and $\h$ be a Hilbert space. We study the generalized bi-Fourier-Stieltjes algebra $B^2(\G\times\GG,\BH)$ by the space of all bi-operator coefficients of unitary representations of $\G$ and $\GG$: $\phi\in B^2(\G\times\GG,\BH)$ if there exists unitary representations $\pi_i:\textbf{G}_i\to \textbf{B}(\h_i)$ and a diagram of bounded operators \[\h\stackrel{V_2}{\To}\hhh\stackrel{T}{\To}\hh\stackrel{V^*_1}{\To}\h\] such that $\phi(s,t)=V^*_1\pi_1(s) T\pi_2(t) V_2 $. We extend the pointwise product on $B^2(\G\times\GG,\BH)$ under which the generalized bi-Fourier-Stieltjes algebra is a completely contractive commutative Banach algebra. We obtain a (tensor type) decomposition by which a well-behaved diagram of its subalgebras will be introduced