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Abstract
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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.
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