| Title:
|
Almost periodic compactifications of group extensions (English) |
| Author:
|
Junghenn, H. D. |
| Author:
|
Milnes, P. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
237-254 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$. Given a property $\mathcal P$ of group compactifications, one can ask whether there exist compactifications $N^{\prime }$ and $K^{\prime }$ of $N$ and $K$ such that the universal $\mathcal P$-compactification of $G$ is canonically isomorphic to an extension of $N^{\prime }$ by $K^{\prime }$. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $\mathcal P$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$. (English) |
| Keyword:
|
group extension |
| Keyword:
|
semidirect product |
| Keyword:
|
topological group |
| Keyword:
|
semitopological semigroup |
| Keyword:
|
right topological semigroup |
| Keyword:
|
compactification |
| Keyword:
|
almost periodic |
| Keyword:
|
weakly almost periodic |
| Keyword:
|
strongly almost periodic |
| MSC:
|
22A20 |
| MSC:
|
22D05 |
| MSC:
|
43A60 |
| idZBL:
|
Zbl 1011.22001 |
| idMR:
|
MR1905433 |
| . |
| Date available:
|
2009-09-24T10:50:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127714 |
| . |
| Reference:
|
[1] J. F. Berglund, H. D. Junghenn and P. Milnes: Analysis on Semigroups: Function Spaces, Compactifications, Representations.Wiley, New York, 1989. MR 0999922 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] M. Rieffel: $C^{\star }$-algebras associated with irrational rotation algebras.Pacific J. Math. 93 (1981), 415–429. Zbl 0499.46039, MR 0623572, 10.2140/pjm.1981.93.415 |
| Reference:
|
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| Reference:
|
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| . |
