| Title:
|
States on unital partially-ordered groups (English) |
| Author:
|
Dvurečenskij, Anatolij |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
[297]-318 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study states on unital po-groups which are not necessarily commutative as normalized positive real-valued group homomorphisms. We show that in contrast to the commutative case, there are examples of unital po-groups having no state. We introduce the state interpolation property holding in any Abelian unital po-group, and we show that it holds in any normal-valued unital $\ell $-group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state space of unital po-groups. (English) |
| Keyword:
|
non-commutative group |
| Keyword:
|
partially ordered groups |
| MSC:
|
06B10 |
| MSC:
|
06F15 |
| idZBL:
|
Zbl 1265.06052 |
| idMR:
|
MR1944311 |
| . |
| Date available:
|
2009-09-24T19:46:07Z |
| Last updated:
|
2015-03-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135465 |
| . |
| Reference:
|
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| . |
