$L^{1}(G)$ as an ideal in its second dual space
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- by Michael Grosser
- Proc. Amer. Math. Soc. 73 (1979), 363-364
- DOI: https://doi.org/10.1090/S0002-9939-1979-0518521-9
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Abstract:
Based on general results on Banach modules a short proof of the following criterion due to S. Watanabe [5] is given: A group algebra ${L^1}(G)$ is a two-sided ideal in its second dual space (equipped with one of the Arens products) if and only if G is compact.References
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- Marc A. Rieffel, Multipliers and tensor products of $L^{p}$-spaces of locally compact groups, Studia Math. 33 (1969), 71–82. MR 244764, DOI 10.4064/sm-33-1-71-82
- Seiji Watanabe, A Banach algebra which is an ideal in the second dual space, Sci. Rep. Niigata Univ. Ser. A 11 (1974), 95–101. MR 383079 —, A Banach algebra which is an ideal in the second dual space. II, Sci. Rep. Niigata Univ. Ser. A 13 (1976), 43-48.
- Pak-ken Wong, On the Arens product and annihilator algebras, Proc. Amer. Math. Soc. 30 (1971), 79–83. MR 281005, DOI 10.1090/S0002-9939-1971-0281005-2
Bibliographic Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 363-364
- MSC: Primary 43A20; Secondary 46H25
- DOI: https://doi.org/10.1090/S0002-9939-1979-0518521-9
- MathSciNet review: 518521