Weighted group algebra as an ideal in its second dual space

Ghahramani, F.

doi:10.1090/S0002-9939-1984-0722417-9

Weighted group algebra as an ideal in its second dual space
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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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A Banach algebra which is an ideal in the second dual space

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