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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Weighted group algebra as an ideal in its second dual space
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by F. Ghahramani PDF
Proc. Amer. Math. Soc. 90 (1984), 71-76 Request permission

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
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 71-76
  • MSC: Primary 43A22; Secondary 43A15, 46J99, 47B99
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0722417-9
  • MathSciNet review: 722417