| Title:
|
Ordering of observables and characterization of conditional expectation (English) |
| Author:
|
Nánásiová, Oľga |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1987 |
| Pages:
|
323-340 |
| . |
| Category:
|
math |
| . |
| MSC:
|
03G12 |
| MSC:
|
06C15 |
| MSC:
|
81P10 |
| MSC:
|
81P20 |
| idZBL:
|
Zbl 0642.03037 |
| idMR:
|
MR916940 |
| . |
| Date available:
|
2009-09-25T10:03:54Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/129507 |
| . |
| Reference:
|
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| Reference:
|
[2] DOOB J. L.: Stochastic Processes.London, 1953. Zbl 0053.26802, MR 0058896 |
| Reference:
|
[3] DVUREČENSKIJ A., PULMANNOVÁ S.: On the sum of observables in a logic.Math. Slovaca 30, 1980, 393-399. Zbl 0454.03030, MR 0595300 |
| Reference:
|
[4] GUDDER S. P.: Hilbert space, independence, and generalized probability.J. of Math. Analysis and Applications 20, 1961, 48-61. MR 0222924 |
| Reference:
|
[5] GUDDER S. P.: Spectral methods for a generalized probability theory.Trans. AMS 119, 1965, 428-442. Zbl 0161.46105, MR 0183657 |
| Reference:
|
[6] GUDDER S. P.: Uniqueness and existence properties of bounded observables.Pac. J. of Math. 19, 1966, 81-93, 588-590. Zbl 0149.23603, MR 0201146 |
| Reference:
|
[7] GUDDER S. P.: Generalized measure theory.Found. Physics 3, 1973, 399-411. MR 0522332 |
| Reference:
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[8] GUDDER S. P., MULLIKIN H. C.: Measure theoretic convergences of observables and operators.J. Math. Phys. 14, 1973, 234-242. MR 0334747 |
| Reference:
|
[9] GUDDER S. P.: Expectation and transition probability.Int. J. of Theor. Physics 20, 1981, 383-395. Zbl 0483.03041, MR 0630220 |
| Reference:
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[10] GUDDER S. P., ZERBE J.: Generalized monotone convergence and Radon-Nikodym theorems.J. Math. Phys. 22, 1981, 2553-2561. Zbl 0467.60003, MR 0640666 |
| Reference:
|
[11] HALMOS P. R.: Measure Theory.New Yoгk, 1950. Zbl 0040.16802, MR 0033869 |
| Reference:
|
[12] HARMAN B., RIEČAN B.: Martingale convergence in q.m. logic.Trans. 9th Prague Conf. on Inf. Theory, Prague 1983. |
| Reference:
|
[13] LOOMIS S.: On the repгesentation of σ-complete Boolean algebras.Bull. AMS. 53, 1947, 757-760. MR 0021084 |
| Reference:
|
[14] NÁNÁSIOVÁ O., PULMANNOVÁ S.: Relative conditional expectations on a logic.Aplikace matematiky 30, 1985, 332-350. Zbl 0585.60003, MR 0806831 |
| Reference:
|
[15] NEUBRUNN T., RIEČAN B.: Miera a integral.VEDA, Bratislava, 1981. MR 0657765 |
| Reference:
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[16] PTÁK P.: Spaces of observables.Czechoslovak Math. Journal 34, 1984, 552-561. Zbl 0572.28007, MR 0764437 |
| Reference:
|
[17] PULMANNOVÁ S.: Compatibility and partial compatibility in quantum logics.Ann. Inst. H. Poincaré 34, 1981, 391-403. MR 0625170 |
| Reference:
|
[18] NEUBRUNN T., PULMANNOVÁ S.: On compatibility in quantum logic.Acta Math. Univ. Comenian XLII-XLIII, 1984, 153-168. MR 0740744 |
| Reference:
|
[19] SHU-TEN CHEN MOY: Characterization of conditional expectation as a transformation space.Pacif. J. Math. 4, 1954, 47-64. MR 0060750 |
| Reference:
|
[20] VARADARAJAN V.: Geometry of quantum theory 1.Von Nonstrand 1968. |
| Reference:
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[21] ZIERLER N.: Order properties of bounded observables.Proc. AMS 14, 1963, 346-351. Zbl 0135.44303, MR 0145863 |
| Reference:
|
[22] SIKORSKI R.: Boolean Algebras.New York, Springer-Verlag. 1969. Zbl 0191.31505, MR 0242724 |
| . |
