| Title:
|
Sum of observables in fuzzy quantum spaces (English) |
| Author:
|
Dvurečenskij, Anatolij |
| Author:
|
Tirpáková, Anna |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
40-50 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory. (English) |
| Keyword:
|
fuzzy quantum space |
| Keyword:
|
observable |
| Keyword:
|
sum of observables |
| MSC:
|
03B52 |
| MSC:
|
03E72 |
| MSC:
|
04A72 |
| MSC:
|
60A99 |
| MSC:
|
81B10 |
| MSC:
|
81P10 |
| idZBL:
|
Zbl 0753.60005 |
| idMR:
|
MR1152156 |
| DOI:
|
10.21136/AM.1992.104490 |
| . |
| Date available:
|
2008-05-20T18:43:00Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104490 |
| . |
| Reference:
|
[1] A. Dvurečenskij, F. Chovanec: Fuzzy quantum spaces and compatibility.Inter. J. Theor. Phys. 27(1988), 1069-1082. MR 0967421 |
| Reference:
|
[2] A. Dvurečenskij, B. Riečan: On joint observables for F-quantum spaces.Busefal 35 (1988), 10-14. |
| Reference:
|
[3] A. Dvurečenskij, B. Riečan: On joint distribution of observables for F-quantum spaces.Fuzzy Sets and Systems 39 (1991), 67-73. MR 1089012, 10.1016/0165-0114(91)90066-Y |
| Reference:
|
[4] W. Guz: Fuzzy $\sigma$-algebras of physics.Inter. J. Theor. Phys. 24 (1985), 481-493. Zbl 0575.46052, MR 0798920 |
| Reference:
|
[5] A. N. Kolmogorov: Grundebegriffe der Wahrscheinlichkeitsrechnung.Berlin, 1933. |
| Reference:
|
[6] J. von Neumann: Mathematische Grundlagen der Quantenmechanik.Springer, Berlin, 1932. MR 0223138 |
| Reference:
|
[7] K. Piasecki: Probability of fuzzy events defined as denumerable additivity measure.Fuzzy Sets and Systems 17 (1985), 271-284. Zbl 0604.60005, MR 0819364, 10.1016/0165-0114(85)90093-4 |
| Reference:
|
[8] J. Pykacz: Quantum logics and soft fuzzy probability spaces.Busefal 32 (1987), 150-157. Zbl 0662.03055 |
| Reference:
|
[9] B. Riečan: A new approach to some basic notions of statistical quantum theory.Busefal 35 (1987), 4-6. |
| Reference:
|
[10] R. Sikorski: Boolean algebras.Springer-Verlag, 1964. Zbl 0123.01303, MR 0126393 |
| Reference:
|
[11] P. Suppes: The probability argument for a nonclassical logic of quantum mechanics.Phil. Sc. 33 (1966), 14-21. MR 0215575, 10.1086/288067 |
| Reference:
|
[12] V. S. Varadarjan: Geometry of quantum theory.Van Nostrand, New Jersey, 1968. |
| Reference:
|
[13] L. A. Zadeh: Probability measures on fuzzy events.J. Math. Anal. Appl. 23 (1968), 421-427. MR 0230569, 10.1016/0022-247X(68)90078-4 |
| . |
