Quantum logics, vector-valued measures and representations
Sylvia Pulmannová; Anatolij Dvurečenskij
Annales de l'I.H.P. Physique théorique (1990)
- Volume: 53, Issue: 1, page 83-95
- ISSN: 0246-0211
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topPulmannová, Sylvia, and Dvurečenskij, Anatolij. "Quantum logics, vector-valued measures and representations." Annales de l'I.H.P. Physique théorique 53.1 (1990): 83-95. <http://eudml.org/doc/76496>.
@article{Pulmannová1990,
author = {Pulmannová, Sylvia, Dvurečenskij, Anatolij},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Relations between vector-valued measures and Hilbert space representations of quantum logics; Segal product},
language = {eng},
number = {1},
pages = {83-95},
publisher = {Gauthier-Villars},
title = {Quantum logics, vector-valued measures and representations},
url = {http://eudml.org/doc/76496},
volume = {53},
year = {1990},
}
TY - JOUR
AU - Pulmannová, Sylvia
AU - Dvurečenskij, Anatolij
TI - Quantum logics, vector-valued measures and representations
JO - Annales de l'I.H.P. Physique théorique
PY - 1990
PB - Gauthier-Villars
VL - 53
IS - 1
SP - 83
EP - 95
LA - eng
KW - Relations between vector-valued measures and Hilbert space representations of quantum logics; Segal product
UR - http://eudml.org/doc/76496
ER -
References
top- [1] A. Alfsen, F. Shultz and E. Stormer, A Gelfand-Neumark theorem for Jordan algebras, Adv. Math., Vol. 28, 1978, pp. 11-56. Zbl0397.46065MR482210
- [2] E. Beltrametti and G. Cassinelli, The logic of quantum mechanics, Addison-Wesley, Reading, Mass., 1981. Zbl0595.03062MR635780
- [3] G. Birkhoff, Lattice theory (Russian translation: Teorija rešetok) Nauka, Moscow, 1984. MR751233
- [4] O. Bratteli and D. Robinson, Operator algebras and quantum statistical mechanics (Russian translation: Operatornyje algebry i kvantovaja statističeskaja mechanika) Mir, Moscow, 1982. Zbl0523.46043MR701539
- [5] E. Christensen, Measures on projections and physical states, Commun. Math. Phys., Vol. 86, 1982, pp. 529-538. Zbl0507.46052MR679201
- [6] A. Dvurečenskij, On convergences of signed states, Math. Slovaca, Vol. 28, 1978, pp. 289-295. Zbl0421.28003MR534996
- [7] A. Dvurečenskij and S. Pulmannová, Random measures on a logic, Demonstratio Math., Vol. 14, 1981, pp. 305-320. Zbl0474.03034MR632289
- [8] A. Dvurečenskij and S. Pulmannova, On joint distributions of observables, Math. Slovaca, Vol. 32, 1982, pp. 155-166. Zbl0495.60007MR658249
- [9] A. Dvurečenskij and S. Pulmannova, State on splitting subspaces and completeness of inner product spaces, Int. J. Theor. Phys., Vol. 27, 1988, pp. 1059-1067. Zbl0661.46019MR967420
- [10] R. Greechie, Orthomodular lattices admitting no states, J. Combinat. Theor., Vol. 10, 1971, pp. 119-132. Zbl0219.06007MR274355
- [11] S. Gudder, Uniqueness and Existence properties of bounded observables, Pac. J. Math., Vol. 19, 81-95, 1966, pp. 588-589. Zbl0149.23603MR201146
- [12] J. Hamhalter, States on W*-algebras and orthogonal vector measures, Preprint ČVUT Praha, 1989. MR1036987
- [13] J. Hamhalter and P. Pták, Hilbert-space valued states on quantum logics, Preprint ČVUT Praha, 1989. Zbl0767.03034MR1152157
- [14] R. Jajte and A. Paszkiewicz, Vector measures on closed subspaces of a Hilbert space, Studia Math., Vol. 58, 1978, pp. 229-251. Zbl0407.46058MR632053
- [15] R. Kadison and J. Ringrose, Fundamentals of the theory of operator algebras, Vol. I, Acad. Press, New York, 1983. Zbl0518.46046MR719020
- [16] P. Kruszynski, Vector measures on orthocomplemented lattices, Math. Proc., Vol. A91 , 1988, pp. 427-442. Zbl0819.46036MR976526
- [17] M. Loeve, Probability theory (Russian translation: Teorija rešetok), Izd. Inostr. Lit., Moskva, 1962. MR140129
- [18] M.C. Matveichuk, Opisanije konečnych mer v polokonečnych algebrach, Funkcional. Analiz Priloženija, Vol. 15, 1981, pp. 41-53.
- [19] R. Mayet, Classes équationelles et équations liées aux états à valeurs dans un espace de Hilbert, Thèse Docteur d'État ès Sciences, Université Claude-Bernard - Lyon, France, 1987.
- [20] A. Paszkiewicz, Measures on projections of von Neumann algebras, J. Funct. Anal., Vol. 62, 1985, pp. 87-117. MR790772
- [21] V.S. Varadarajan, Geometry of quantum theory, Springer, New York, 1985. Zbl0581.46061MR805158
- [22] F. Yeadon, Measures on projections in W*-algebras of type II, Bull. London Math. Soc., Vol. 15, 1983, pp. 139-145. Zbl0522.46045MR689246
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