Let A be a completely contractive Banach algebra. For any index set I
we consider the space of bounded I X I-matrices with entries in A.
Under Schur multiplication, this space of matrices is itself a
completely contractive Banach algebra. In particular, for any locally compact
group, we obtain natural operator-valued Fourier-Stieltjes and measure
algebras. This is joint work with G. A. Bagheri-Bardi and A. R.