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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Which amalgams are convolution algebras?


Authors: James Stewart and Saleem Watson
Journal: Proc. Amer. Math. Soc. 93 (1985), 621-627
MSC: Primary 43A15
MathSciNet review: 776191
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Abstract: We determine necessary and sufficient conditions on a locally compact abelian group $ G$ for the amalgam $ \left( {{L^p},{l^q}} \right)\left( G \right)$ to be an algebra under convolution. If $ q > 1,G$ must be compact; if $ p < 1,G$ must be discrete. If $ p \geqslant 1$ and $ q \leqslant 1$, the amalgam is always an algebra.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0776191-1
PII: S 0002-9939(1985)0776191-1
Keywords: Amalgam, convolution algebra
Article copyright: © Copyright 1985 American Mathematical Society