Σ * -algèbres, probabilités non commutatives et applications
Contributions au calcul des probabilités, Mémoires de la Société Mathématique de France, no. 35 (1973), pp. 145-189.
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     author = {Dang Ngoc Nghiem},
     title = {$\Sigma ^\ast $-alg\`ebres, probabilit\'es non commutatives et applications},
     booktitle = {Contributions au calcul des probabilit\'es},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     pages = {145--189},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {35},
     year = {1973},
     doi = {10.24033/msmf.118},
     mrnumber = {56 #9283},
     zbl = {0288.46059},
     url = {http://www.numdam.org/articles/10.24033/msmf.118/}
}
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Dang Ngoc Nghiem. $\Sigma ^\ast $-algèbres, probabilités non commutatives et applications, in Contributions au calcul des probabilités, Mémoires de la Société Mathématique de France, no. 35 (1973), pp. 145-189. doi : 10.24033/msmf.118. http://www.numdam.org/articles/10.24033/msmf.118/

(1) Banach & Kuratowski : Sur une généralisation du problème de la mesure. Fund. Math. 14 (1929) 127-131. | JFM

(2) Berberian S.K. : Notes on spectral Theory (Van Nostrand 1966). | MR | Zbl

(3) Bodiou G.: Théorie dialectique des probabilités englobant leurs calculs classique et quantique (Gauthier-Villars) 1964. | MR | Zbl

(4) Davies E.B. : On the Borel structure of C*-algebras (with an appendix by R.V. KADISON). Comm. Math. Phys. 8 (1968) 147-164. | MR | Zbl

(5) Davies E.B.: The structure of ∑*-algebras. Quart. J. Math. 20 (1969) 351-366. | MR | Zbl

(6) Davies E.B. Quantum Stochastic Processes. Comm. Math. Phys. 15 (1969) 277-304. | MR | Zbl

(7) Deny J. : Les noyaux élémentaires. Séminaire de Théorie du Potentiel (Brelot-Choquet-Deny). (1959-1960). | Numdam

(8) Dixmier J. Les algèbres d'opérateurs dans l'espace hilbertien. (Gauthier-Villars) (1969). | Zbl

(9) Dixmier J. Les C*-algèbres et leurs représentations. (Gauthier-Villars) (1969). | MR | Zbl

(10) Doplicher, Kastler & Størmer : Invariant states and asymptotic abelianness. J. Func. Ana. 3 (1969) 419-434. | MR | Zbl

(11) Dynkin E.B.: Theory of Markov Processes I & II. Springer-Verlag (1965).

(12) Edwards C.M. : The operational approach to algebraic quantum theory. Comm. Math. Phys. 16 (1970) 207-230. | MR | Zbl

(13) Effros E.G.: Order Ideals in a C*-algebra and its dual. Duke Math. J. 30 (1963) 391-411. | MR | Zbl

(14) Golodets V. Ya : Classification of representations of the anticommutation relations. Russian Math. Surveys 24 (1969) 1-64. | Zbl

(15) Guichardet A : Algèbres d'observables associées aux relations de commutation. (Armand Colin). | Zbl

(16) Guichardet A.: Sur la catégorie des algèbres de Von Neumann. Bull. Sci. Math. 90 (1966), 41-64. | MR | Zbl

(17) Guichardet A.: Leçons sur certaines algèbres topologiques. (Gordon & Breach) (1967). | Zbl

(18) Guichardet A. : Tensor Products of C*-algebras. I. Lecture Notes Series 13 Aarhus Universitet (1969). | Zbl

(19) Guichardet A. : Tensor Products of C*-algebras. II. Lecture Notes Series 13 Aarhus Universitet (1969). | Zbl

(20) Guichardet A. & Kastler D. : Désintégration des états quasi-invariants des C*-algèbres. Journ. Math. Pures et Appl. 49 (1970) 349-380. | MR | Zbl

(21) Haag, Kadison & Kastler : Nets of C*-algebras and classification of states. Comm. Math. Phys. 16 (1970) 81-104. | MR | Zbl

(22) Haag & Kastler : An algebraic approach to quantum field theory. J. Math. Phys. 5 (1964) 848-861. | MR | Zbl

(23) Halmos P.R. : Measure Theory. (Van Nostrand) (1961).

(24) Halmos P.R. : Lectures on Boolen algebras (Van Nostrand Math. Studies) (1963). | Zbl

(25) Kadison R.V. : Transformation of states in operator theory and dynamics. Topology 3, Suppl. 2 (1965) 177-198. | MR | Zbl

(26) Kadison R.V. : States and Representations. T.A.M.S. 103 (1962) 304-319. | MR | Zbl

(27) Kadison R.V. : Operator algebras with a faithful weakly closed representation. Ann. Math. 64 (1954) 175-181. | MR | Zbl

(28) Landford O. & D. Ruelle : Integral representations of invariant states on B*-algebras. J. Math. Phys. 8 (1967) 1460-1463. | MR | Zbl

(29) Loomis L.H. : On the representation of σ-complete Boolean algebras. Bull. Amer. Math. Soc. 53 (1947) 757-760. | MR | Zbl

(30) Loomis L.H. : Abstract harmonic analysis. (D. Van Nostrand Company) (1953). | MR | Zbl

(31) Mackey G.W. : Mathematical foundations of Quantum Mechanics. (W.A. Benjamin, Inc.) (1963). | Zbl

(32) Meyer P.A. : Probabilités et Potentiels (Hermann, 1966). | MR | Zbl

(33) Mitchell : Theory of categories (Academic Press, 1965). | Zbl

(34) Neveu J. : Bases mathématiques du Calcul des Probabilités. (Masson, 1970). | MR | Zbl

(35) Pedersen G.K. : On weak and σ-monotone closures of C*-algebras. Comm. Math. Phys. 11 (1969) 221-266. | MR | Zbl

(36) Pedersen G.K. : C*-integrals (Kobenhavns Universitet, May 1970). | MR | Zbl

(37) Plymen R. : C*-algebras and Mackey's axioms. Comm. Math. Phys. 8 (1968) 132-146. | MR | Zbl

(38) Ruelle D. : Statistical Mechanics (Benjamin, New York, 1969). | MR | Zbl

(39) Ruelle D. : Integral representation of states on a C*-algebras. J. Func. Ana. 6 (1970) 116-151. | MR | Zbl

(40) Sakai S. : On the central decomposition of positive functionals on C*-algebras. T.A.M.S. 118 (1965) 406-419. | MR | Zbl

(41) Sakai S. : On topological properties of W*-algebras. Proc. Japan Acad. 33 (1957) 439-444. | MR | Zbl

(42) Sakai S. : C*-algebras and W*-algebras. Springer-Verlag (1971). | MR | Zbl

(43) Segal I.E. : Postulates for general quantum mechanics. Ann. of Math. 4 (1947), 930-948. | MR | Zbl

(44) Segal I.E. & Kunze : Integrals and Operators (Mc GrawHill) (1968). | MR | Zbl

(45) Størmer E. : States and invariant maps of operator algebras. J. Func. Ana. 5 (1970) 44-65. | MR | Zbl

(46) Takeda Z. : On the representation of operator algebras. Proc. Japan Acad. 30 (1954) 299-304. | MR | Zbl

(47) Takeda Z. : On the representations of operator algebras II. Tohôku Math. J. 6 (1954), 212-219. | MR | Zbl

(48) Takeda Z. : Inductive limit and infinite direct product of operator algebras. Tohôku Math. J. 7 (1955) 67-86. | MR | Zbl

(49) Turumaru T. : On the direct product of operator algebras. I. Tohôku Math. J. 4 (1952) 242-251. | MR | Zbl

(50) Turumaru T. : On the direct product of operator algebras II. Tohôku Math. J. 5 (1953) 1-7. | MR | Zbl

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