## Normal structure in dual Banach spaces associated with a locally compact group

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- by Anthony To Ming Lau and Peter F. Mah
- Trans. Amer. Math. Soc.
**310**(1988), 341-353 - DOI: https://doi.org/10.1090/S0002-9947-1988-0937247-0
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## Abstract:

In this paper we investigated when the dual of a certain function space defined on a locally compact group has certain geometric properties. More particularly, we asked when weak$^{*}$ compact convex subsets in these spaces have normal structure, and when the norm of these spaces satisfies one of several types of Kadec-Klee property. As samples of the results we have obtained, we have proved, among other things, the following two results: (1) The measure algebra of a locally compact group has weak$^{*}$-normal structure iff it has property SUKK$^{*}$ iff it has property SKK$^{*}$ iff the group is discrete; (2) Among amenable locally compact groups, the Fourier-Stieltjes algebra has property SUKK$^{*}$ iff it has property SKK$^{*}$ iff the group is compact. Consequently the Fourier-Stieltjes algebra has weak$^{*}$-normal structure when the group is compact.## References

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## Bibliographic Information

- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**310**(1988), 341-353 - MSC: Primary 43A10; Secondary 43A15, 46B20
- DOI: https://doi.org/10.1090/S0002-9947-1988-0937247-0
- MathSciNet review: 937247