Abstract
Let G denote a compact abelian group and B a Banach algebra of continuous functions defined on G with pointwise multiplication. G.E. Silov called B of type C if its norm is equivalent to that defined by \[ \|b\|^c = sup \hspace{0.1in} inf\{\|c\|_B : c \in B\hspace{0.1in} ,\hspace{0.1in} c(x) = b(x)\}\hspace{0.1in} ,\hspace{0.1in} x \in G \] and gave a complete classification of those algebras which are homogeneous and of type C. In this paper, we first replace pointwise multiplication by convolution, before generalizing the notion of type C to homogeneous Banach spaces. Again a complete classification is obtained.
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