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.
Information
Published: 1 January 1987
First available in Project Euclid: 18 November 2014
zbMATH: 0653.46028
MathSciNet: MR935609
Rights: Copyright © 1987, Centre for Mathematical Analysis, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
