| Title:
|
Observables on $\sigma $-MV algebras and $\sigma $-lattice effect algebras (English) |
| Author:
|
Jenčová, Anna |
| Author:
|
Pulmannová, Silvia |
| Author:
|
Vinceková, Elena |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
541-559 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Effect algebras were introduced as abstract models of the set of quantum effects which represent sharp and unsharp properties of physical systems and play a basic role in the foundations of quantum mechanics. In the present paper, observables on lattice ordered $\sigma$-effect algebras and their “smearings” with respect to (weak) Markov kernels are studied. It is shown that the range of any observable is contained in a block, which is a $\sigma$-MV algebra, and every observable is defined by a smearing of a sharp observable, which is obtained from generalized Loomis-Sikorski theorem for $\sigma$-MV algebras. Generalized observables with the range in the set of sharp real observables are studied and it is shown that they contain all smearings of observables. (English) |
| Keyword:
|
lattice effect algebra |
| Keyword:
|
MV algebra |
| Keyword:
|
observable |
| Keyword:
|
state |
| Keyword:
|
Markov kernel |
| Keyword:
|
weak Markov kernel |
| Keyword:
|
smearing |
| Keyword:
|
generalized observable |
| MSC:
|
03G12 |
| MSC:
|
81P10 |
| MSC:
|
81P15 |
| idZBL:
|
Zbl 1237.81008 |
| idMR:
|
MR2884860 |
| . |
| Date available:
|
2011-09-23T11:22:13Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141658 |
| . |
| Reference:
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