| Title:
|
On Kalmbach measurability (English) |
| Author:
|
d'Andrea, A. B. |
| Author:
|
de Lucia, P. |
| Author:
|
Wright, J. D. Maitland |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
6 |
| Year:
|
1994 |
| Pages:
|
445-447 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we show that, for an arbitrary orthomodular lattice $L$, when $\mu $ is a faithful, finite-valued outer measure on $L$, then the Kalmbach measurable elements of $L$ form a Boolean subalgebra of the centre of $L$. (English) |
| Keyword:
|
Kalmbach measurability |
| Keyword:
|
Boolean algebra |
| Keyword:
|
orthomodular lattice |
| MSC:
|
06C15 |
| MSC:
|
28A60 |
| idZBL:
|
Zbl 0815.28004 |
| idMR:
|
MR1298732 |
| DOI:
|
10.21136/AM.1994.134270 |
| . |
| Date available:
|
2009-09-22T17:45:39Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134270 |
| . |
| Reference:
|
[1] E. Beltrametti, G. Cassinelli: The logic of quantum mechanics.Addison Wesley, Reading MA, 1981. MR 0635780 |
| Reference:
|
[2] L. Beran: Orthomodular Lattices.Algebraic approach, Academia, Prague and Reidel, Dordrecht, 1984. MR 0785005 |
| Reference:
|
[3] S. Gudder: Stochastic methods in quantum mechanics.North-Holland, Amsterdam, 1979. Zbl 0439.46047, MR 0543489 |
| Reference:
|
[4] G. Kalmbach: Orthomodular lattices.Academic Press, London, 1983. Zbl 0528.06012, MR 0716496 |
| Reference:
|
[5] G. Kalmbach: Quantum measure spaces.Foundations of Phys. 20 (1990), 801–821. MR 1067216, 10.1007/BF01889692 |
| Reference:
|
[6] P. Pták, S. Pulmannova: Orthomodular structures as quantum logics.Kluwer, Dordrecht, 1991. MR 1176314 |
| Reference:
|
[7] V. S. Varadarajan: Geometry of quantum theory.Springer-Verlag, Berlin, 1985. Zbl 0581.46061, MR 0805158 |
| . |
