Complete sets of non-self-adjoint observables: An unbounded approach

Journal of Mathematical Physics

Volumn 37, Issue 3, 1996, Pages 1148-1160

  Epifanio, Giuseppina ^a   Todorov, Todor S ^b   Trapani, Camillo ^a  

^a UNIVERSITY OF PALERMO   (Italy)

^b INSTITUTE FOR NUCLEAR RESEARCH AND NUCLEAR ENERGY   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030551105     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531452     Document Type: Article

References (38)

1. E. B. Davies, Quantum Theory of Open Systems (Academic, London, 1976).
2. D. A. Dubin and M. A. Hennings, Quantum Mechanics, Algebras and Distributions, Pitman Research Notes in Mathematics (Longman, Harlow, 1990).
3. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
4. G. Ludwig, Foundations of Quantum Mechanics (Springer-Verlag, New York, 1983).
5. S. T. Ali, "Stochastic Localization, Quantum Mechanics on Phase Space and Quantum Space Time," Riv. Nuovo Cimento 8, 1-128 (1985).
6. E. B. Davis, "Generators of Dynamical Semigroups," J. Fund. Anal. 34, 421-432 (1979).
7. L. Accardi, A. Frigerio, and J. T. Lewis, "Quantum Stochastic Processes," Publ. RIMS Kyoto Univ. 18, 97-133 (1982).
8. S. T. Ali and G. G. Emch, "Fuzzy observables in quantum mechanics," J. Math. Phys. 15, 176-182 (1974).
9. E. B. Davis, "On repeated measurements of continuous observables in quantum mechanics," J. Funct. Anal. 6, 318-346 (1970).
10. J. M. Jauch and C. Piron, "Generalized localizability," Helv. Phys. Acta 40, 559-577 (1967).
11. W. O. Amrein, "Localizability of particles with zero mass," Helv. Phis. Acta 42, 149-190 (1969).
12. D. P. L. Castrigiano, "On Euclidean systems of covariance for massless particles," Lett. Math. Phys. 5, 303-309 (1981).
13. E. B. Davis and J. T. Lewis, "An operational approach to quantum probability," Commun. Math. Phys. 17, 239-260 (1970).
14. K. Kraus, Operations and Effects in Hilbert space Formulation of Quantum Theory," Lecture Notes in Physics, Vol. 29 (Springer-Verlag, New York, 1974).
15. F. Riesz and B. Sz. Nagy, Leçons d'Analyse Fonctionelle (Gauthier-Villars, Paris, 1972).
16. E. B. Davis, "Quantum communication systems," IEEE Trans. Inform. Theory IT-23 (7), 530-534 (1977).
17. H. D. Doebner and T. S. Todorov, "On the method of quantization of generalized observables in Quantum Mechanics," Clausthal-Sofia preprint, 1983.
18. G. Epifanio, T. S. Todorov, and C. Trapani, "Complete sets of compatible non self-adjoint observables," Helv. Phys. Acta 65, 1-10 (1992).
19. T. S. Todorov, "On some physical and mathematical aspects of generalized observables in quantum theory," Preprint Göttingen.
20. J. M. Jauch, "Systems of observables in quantum mechanics," Helv. Phys. Acta 33, 711 (1960).
21. J.-P. Antoine, G. Epifanio, and C. Trapani, "Complete sets of unbounded observables," Helv. Phys. Acta 56, 1175-1186 (1983).
22. K. Schmüdgen, Unbounded Operator Algebras and Representation Theory (Birkäuser, Basel, 1990).
23. G. Epifanio and C. Trapani, "V* algebras: A particular class of unbounded operator algebras," J. Math. Phys. 25, 2633-2637 (1984).
24. E. Prugovecki, Quantum Mechanics in Hilbert Space (Academic, New York, 1971).
25. Y. S. Samoilenko, Spectral Theory of Families of Self-Adjoint Operators (Kluwer, Dordrecht, 1991).
26. J.-P. Antoine and W. Karwowski, "Partial *-algebras of closed linear operators in Hilbert space," Publ. RIMS 21, 205-236 (1985).
27. J.-P. Antoine and F. Mathot, "Partial *-algebras of closed operators and their commutants I. General structure," Ann. Inst. H. Poincaré 46, 299-324 (1987).
28. J.-P. Antoine, F. Mathot, and C. Trapani, "Partial *-algebras of closed operators and their commutants II. Commutants and bicommutants," Ann. Inst. H. Poincaré 46, 325-351 (1987).
29. L-P. Antoine and K. Karwowski, "Commuting normal operators in partial O*-algebras," Ann. Inst. H. Poincaré 50, 161-185 (1989).
30. J.-P. Antoine, A. Inoue, and C. Trapani, "Partial *-algebras of closable operators I: The basic theory and the Abelian case," Publ. RIMS Kyoto Univ. 26, 359-395 (1990).
31. J.-P. Antoine, A. Inoue, and C. Trapani, "Partial *-algebras of closable operators II. States and representations of partial *-algebras," Publ. RIMS, Kyoto Univ. 27, 399-430 (1991).
32. J.-P. Antoine, A. Inoue, and C. Trapani, "Partial *-algebras of closable operators: a review," preprint UCL-IPT-95-08, Rev. Math. Phys. (to appear in 8, 1996).
33. N. I. Akhieser and I. M. Glasman, Theory of Linear Operators in Hilbert space, II (Ungar, New York, 1963).
34. B. Sz-Nagy and C. Foias, Harmonic Analysis of Operators in Hilbert Space (North Holland, Amsterdam, 1970).
35. C. Trapani, "Commutation properties of symmetric operators," Math. Nachrichten 174, 305-315 (1995).
36. A. O. Barut and R. Raczka, Theory of Group Representations and Applications (Polish Scientific, Warszawa, 1980).
37. R. T. Denchev, "On commutativity of self-adjoint extensions of partial differential operators," Matematicheskii sbornik 84, 369 (1978).
38. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics (Springer-Verlag, New York, 1979).