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Normal Structure in Dual Banach Spaces Associated With a Locally Compact Group
| Content Provider | Scilit |
|---|---|
| Author | Lau, Anthony To-Ming Mah, Peter F. |
| Copyright Year | 1988 |
| Description | 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. |
| Related Links | https://www.ams.org/tran/1988-310-01/S0002-9947-1988-0937247-0/S0002-9947-1988-0937247-0.pdf |
| Ending Page | 353 |
| Page Count | 13 |
| Starting Page | 341 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/2001126 |
| Journal | Transactions of the American Mathematical Society |
| Issue Number | 1 |
| Volume Number | 310 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1988-11-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Physics Amenable Group Banach Space Locally Compact Group |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
