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

 

Weighted group algebra as an ideal in its second dual space


Author: F. Ghahramani
Journal: Proc. Amer. Math. Soc. 90 (1984), 71-76
MSC: Primary 43A22; Secondary 43A15, 46J99, 47B99
MathSciNet review: 722417
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Abstract: For a locally compact group $ G$ let $ {L^1}(G,\omega \lambda )$ be a weighted group algebra. We characterize compact and weakly compact multipliers on $ {L^1}(G,\omega \lambda )$. This characterization is employed to find a necessary and sufficient condition for $ {L^1}(G,\omega \lambda )$ to be an ideal in its second dual space, where the second dual is equipped with an Arens product. In the special case where $ \omega (t) = 1(t \in G)$, we deduce a result due to K. P. Wong that if $ G$ is a compact group, then $ {L^1}(G,\lambda )$ is an ideal in its second dual space and its converse due to S. Watanabe.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0722417-9
PII: S 0002-9939(1984)0722417-9
Keywords: Weighted group algebra, compact multiplier, Arens product
Article copyright: © Copyright 1984 American Mathematical Society