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The strong law of large numbers for states and traces of a \(W^*\)-algebra. (English) Zbl 0395.60033

60F15 Strong limit theorems
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
Full Text: DOI
[1] Cuculescu, I.: Martingales on von Neumann algebras. J. Multivariate Anal.1, 17–27 (1971) · Zbl 0254.60031
[2] Dixmier, J.: Formes linéaires sur un anneau d’opérateurs. Bull. Soc. Math. France81, 9–39 (1953) · Zbl 0050.11501
[3] Dixmier, J.: Les algèbres d’opérateurs dans l’espace hilbertien. 2nd ed. Paris: Gauthier-Villars 1969 · Zbl 0175.43801
[4] Doob, J.L.: Stochastic processes. New York: Wiley 1953 · Zbl 0053.26802
[5] Gootman, E.C., Kannan, D.: Zero-one laws in finiteW*-algebras. J. Math. Anal. Appl.55, 743–756 (1976) · Zbl 0337.46052
[6] Guichardet, A.: Tensor products ofC*-algebras II: Infinite tensor products. Aarhus University Lecture Notes 13 (1969) · Zbl 0228.46056
[7] Lance, E.C.: Ergodic theorems for convex sets and operator algebras. Invent. Math.37, 201–214 (1976) · Zbl 0338.46054
[8] Nelson, E.: Notes on non-commutative integration. J. Functional Analysis15, 103–116 (1974) · Zbl 0292.46030
[9] von Neumann, J.: On infinite direct products. Compositio Math.6, 1–77 (1938) · JFM 64.0377.01
[10] Padmanabhan, A.R.: Convergence in measure and related results in finite rings of operators. Trans. Amer. Math. Soc.128, 359–378 (1967) · Zbl 0166.11503
[11] Sakai, S.:C*-algebras andW*-algebras. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0219.46042
[12] Segal, I.E.: A non-commutative extension of abstract integration. Ann. of Math.57, 401–457 (1953) · Zbl 0051.34201
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