Ordering of observables and characterization of conditional expectation

Oľga Nánásiová

Mathematica Slovaca (1987)

  • Volume: 37, Issue: 4, page 323-340
  • ISSN: 0232-0525

How to cite

top

Nánásiová, Oľga. "Ordering of observables and characterization of conditional expectation." Mathematica Slovaca 37.4 (1987): 323-340. <http://eudml.org/doc/31837>.

@article{Nánásiová1987,
author = {Nánásiová, Oľga},
journal = {Mathematica Slovaca},
keywords = {partial compatibility; commutator; ordering of observables; quantum logic; conditional expectation},
language = {eng},
number = {4},
pages = {323-340},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Ordering of observables and characterization of conditional expectation},
url = {http://eudml.org/doc/31837},
volume = {37},
year = {1987},
}

TY - JOUR
AU - Nánásiová, Oľga
TI - Ordering of observables and characterization of conditional expectation
JO - Mathematica Slovaca
PY - 1987
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 37
IS - 4
SP - 323
EP - 340
LA - eng
KW - partial compatibility; commutator; ordering of observables; quantum logic; conditional expectation
UR - http://eudml.org/doc/31837
ER -

References

top
  1. CATLIN D. E., Spectral theory in quantum logics, Int. J. of Theor. Physics, 1, 1968, 3-16. (1968) MR0239833
  2. DOOB J. L., Stochastic Processes, London, 1953. (1953) Zbl0053.26802MR0058896
  3. DVUREČENSKIJ A., PULMANNOVÁ S., On the sum of observables in a logic, Math. Slovaca 30, 1980, 393-399. (1980) Zbl0454.03030MR0595300
  4. GUDDER S. P., Hilbert space, independence, and generalized probability, J. of Math. Analysis and Applications 20, 1961, 48-61. (1961) MR0222924
  5. GUDDER S. P., Spectral methods for a generalized probability theory, Trans. AMS 119, 1965, 428-442. (1965) Zbl0161.46105MR0183657
  6. GUDDER S. P., Uniqueness and existence properties of bounded observables, Pac. J. of Math. 19, 1966, 81-93, 588-590. (1966) Zbl0149.23603MR0201146
  7. GUDDER S. P., Generalized measure theory, Found. Physics 3, 1973, 399-411. (1973) MR0522332
  8. GUDDER S. P., MULLIKIN H. C., Measure theoretic convergences of observables and operators, J. Math. Phys. 14, 1973, 234-242. (1973) MR0334747
  9. GUDDER S. P., Expectation and transition probability, Int. J. of Theor. Physics 20, 1981, 383-395. (1981) Zbl0483.03041MR0630220
  10. GUDDER S. P., ZERBE J., Generalized monotone convergence and Radon-Nikodym theorems, J. Math. Phys. 22, 1981, 2553-2561. (1981) Zbl0467.60003MR0640666
  11. HALMOS P. R., Measure Theory, New Yoгk, 1950. (1950) Zbl0040.16802MR0033869
  12. HARMAN B., RIEČAN B., Martingale convergence in q.m. logic, Trans. 9th Prague Conf. on Inf. Theory, Prague 1983. (1983) 
  13. LOOMIS S., On the repгesentation of σ-complete Boolean algebras, Bull. AMS. 53, 1947, 757-760. (1947) MR0021084
  14. NÁNÁSIOVÁ O., PULMANNOVÁ S., Relative conditional expectations on a logic, Aplikace matematiky 30, 1985, 332-350. (1985) Zbl0585.60003MR0806831
  15. NEUBRUNN T., RIEČAN B., Miera a integral, VEDA, Bratislava, 1981. (1981) MR0657765
  16. PTÁK P., Spaces of observables, Czechoslovak Math. Journal 34, 1984, 552-561. (1984) Zbl0572.28007MR0764437
  17. PULMANNOVÁ S., Compatibility and partial compatibility in quantum logics, Ann. Inst. H. Poincaré 34, 1981, 391-403. (1981) MR0625170
  18. NEUBRUNN T., PULMANNOVÁ S., On compatibility in quantum logic, Acta Math. Univ. Comenian XLII-XLIII, 1984, 153-168. (1984) MR0740744
  19. SHU-TEN CHEN MOY, Characterization of conditional expectation as a transformation space, Pacif. J. Math. 4, 1954, 47-64. (1954) MR0060750
  20. VARADARAJAN V., Geometry of quantum theory 1, Von Nonstrand 1968. (1968) 
  21. ZIERLER N., Order properties of bounded observables, Proc. AMS 14, 1963, 346-351. (1963) Zbl0135.44303MR0145863
  22. SIKORSKI R., Boolean Algebras, New York, Springer-Verlag. 1969. (1969) Zbl0191.31505MR0242724

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.