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Weakly Almost Periodic Functions and Fourier-Stieltjes Algebras of Locally Compact Groups
| Content Provider | Scilit |
|---|---|
| Author | Chou, Ching |
| Copyright Year | 1982 |
| Description | A noncompact locally compact group $G$ is called an Eberlein group if $W(G) = B{(G)^ - }$ where $W(G)$ is the algebra of continuous weakly almost periodic functions on $G$ and $B{(G)^ - }$ is the uniform closure of the Fourier-Stieltjes algebra of $G$. We show that if $G$ is a noncompact $[IN]$-group or a noncompact nilpotent group then $W(G)/B{(G)^ - }$ contains a linear isometric copy of ${l^\infty }$. In particular, $G$ is not an Eberlein group. On the other hand, finite direct products of Euclidean motion groups and, by a result of W. Veech, noncompact semisimple analytic groups with finite centers are Eberlein groups. |
| Related Links | https://www.ams.org/tran/1982-274-01/S0002-9947-1982-0670924-2/S0002-9947-1982-0670924-2.pdf |
| Ending Page | 157 |
| Page Count | 17 |
| Starting Page | 141 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/1999501 |
| Journal | Transactions of the American Mathematical Society |
| Issue Number | 1 |
| Volume Number | 274 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1982-11-01 |
| Access Restriction | Open |
| Subject Keyword | Logic Functions Algebra Noncompact Fourier Stieltjes Finite Nilpotent Semisimple Uniform |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
