Ali Bagheri-Bardi

Let A be a completely contractive Banach algebra. For any index sets I and J we consider the space MI (A) of bounded IJ-matrices with entries in A. Under Schur multiplication, this space of matrices is itself a completely contractive Banach algebra. In particular, for any locally com- pact group, we obtain natural operator-valued Fourier-Stieltjes and measure algebras. We examine their properties in the context of abstract convolution algebras, which are defined via C*-bialgebras.