| Title:
|
Fuzzy equality and convergences for $F$-observables in $F$-quantum spaces (English) |
| Author:
|
Chovanec, Ferdinand |
| Author:
|
Kôpka, František |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
32-45 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce a fuzzy equality for $F$-observables on an $F$-quantum space which enables us to characterize different kinds of convergences, and to represent them by pointwise functions on an appropriate measurable space. (English) |
| Keyword:
|
$F$-quantum space |
| Keyword:
|
$F$-state |
| Keyword:
|
$F$-observable |
| Keyword:
|
representation theorem of $F$-observables |
| Keyword:
|
convergence of $F$-observables |
| Keyword:
|
soft fuzzy $\sigma$-algebras |
| Keyword:
|
fuzzy equalities |
| Keyword:
|
fuzzy inequalities |
| Keyword:
|
fuzzy sets |
| MSC:
|
03E72 |
| MSC:
|
04A72 |
| MSC:
|
28A20 |
| MSC:
|
28E10 |
| idZBL:
|
Zbl 0732.28010 |
| idMR:
|
MR1093481 |
| DOI:
|
10.21136/AM.1991.104442 |
| . |
| Date available:
|
2008-05-20T18:40:53Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104442 |
| . |
| Reference:
|
[1] S. P. Gudder H. C. Mullikin: Measure theoretic convergences of observables and operators.Journal of Mathematical Physics, 14 (1973), 234-242. MR 0334747, 10.1063/1.1666301 |
| Reference:
|
[2] B. Riečan: A new approach to some notions of statistical quantum mechanics.Busefal, 35, (1988), 4-6. |
| Reference:
|
[3] A. Dvurečenskij: On existence of probability measures on fuzzy measurable spaces.(to appear in Fuzzy Sets and Systems). MR 1128000 |
| Reference:
|
[4] K. Piasecki: Probability of fuzzy events defined as denumerable addivity measure.Fuzzy Sets and Systems, 17 (1985), 271-284. MR 0819364, 10.1016/0165-0114(85)90093-4 |
| Reference:
|
[5] A. Dvurečenskij A. Tirpáková: A note on a sum of observables in F-quantum spaces and its applications.Busefal, 35 (1988), 132-137. |
| Reference:
|
[6] K. Piasecki: On fuzzy F-measures.In: Proc. First Winter School on Measure Theory, Liptovský Ján, Jan. 10-15, 1988, 108-112. MR 1000200 |
| Reference:
|
[7] A. Dvurečenskij: On a representation of observables in fuzzy measurable spaces.(to appear in J. Math. Anal. Appl.). MR 1372199 |
| Reference:
|
[8] A. Dvurečenskij B. Riečan: On joint distribution of observables for F-quantum spaces.(to appear in Fuzzy Sets and Systems). MR 1089012 |
| Reference:
|
[9] T. Neubrunn B. Riečan: Measure and Integral.(Slovak). VEDA Bratislava 1981. MR 0657765 |
| . |
