On ergodic theorems for free group actions on noncommutative spaces

Probability Theory and Related Fields

Volumn 135, Issue 4, 2006, Pages 520-546

  Anantharaman Delaroehe, Claire ^a  

^a UNIVERSITÉ D'ORLÉANS   (France)

Author keywords

Free group actions; Noncommutative ergodic theorems

Indexed keywords

EID: 33646744372     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-005-0456-1     Document Type: Article

References (46)

1. Accardi, L., Cecchini, C.: Conditional expectations in von Neumann algebras and a theorem of Takesaki. J. Funct. Anal. 45, 245-273 (1982)
2. Arnol'd, V.I., Krylov, A.L.: Uniform distribution of points on a sphere and certain ergodic properties of solutions of linear ordinary differential equations in acomplex domain. Dokl. Akad. Nauk. SSSR 148, 9-12 (1963)
3. Bhat, B.V.R., Parthasarathy, K.R.: Markov dilations of nonconservative dynamical semi-groups and a quantum boundary theory. Ann. Inst. Henri Poincaré 31, 601-651 (1995)
4. Blanchard, E., Dykema, K.: Embeddings of reduced free products of operator algebras. Pacific J. Math. 199, 1-19 (2001)
5. Bratteli, O., Robinson, D.W.: Operator algebras and quantum stastistical mechanics I. Texts and Monographs in Physics, Springer-Verlag. 1979
6. Bufetov, A.I.: Operator ergodic theorems for actions of free semigroups and groups. Funct. Anal. Appl. 34, 239-251 (2000)
7. Bufetov, A.I.: Convergence of spherical averages for actions of free groups. Annals of Math. 155, 929-944 (2002)
8. Chilin, V.I., Litvinov, S., Skalski, A.: A few new results in noncommutative ergodic theory. To appear in J. Operator Theory
9. Connes, A., Narnhofer, H., Thirring, W.: Dynamical entropy of C*-algebras and von Neumann algebras. Commun. Math. Phys. 112, 691-817 (1987)
10. Conze, J.P., Dang Ngoc, N.: Ergodic theorems for non-commutative dynamical systems. Invent. Math. 46, 1-15 (1978)
11. Dang-Ngoc, N.: Pointwise convergence of martingales in von Neumann algebras. Israel J. Math. 34, 273-280 (1979)
12. Defant, A., Junge, M.: Classical summation methods in noncommutative probability. In preparation
13. Goldstein, S., Lindsay, J.M.: K M S-symmetric Markov semigroups. Math. Zeit. 219, 591-608 (1995)
14. Grigorchuk, R.I.: An individual ergodic theorems for actions of free groups. Proc. XII Workshop in the theory of operators in functional spaces. Tambov, 1987
15. Guivarc'h, Y.: Généralisation d'un théorème de von Neumann. C. R. Acad. Sci. Paris, Ser. A 268, 1020-1023 (1969)
16. Jajte, R.: Strong limit theorems in non-commutative probability. Lecture Notes in Math. 1110, Springer-Verlag, 1985
17. 2-spaces. Lecture Notes in Math. 1477, Springer-Verlag, 1991
18. Junge, M.: Doob's inequality for non-commutative martingales. J. Reine Angew. Math. 549, 149-190 (2002)
19. p non commutatifs. C. R. Acad. Sci. Paris, Ser. 1334, 773-778 (2002)
20. Junge, M., Xu, Q.: Noncommutative maximal ergodic theorems, Preprint 2004
21. Junge, M., Xu, Q.: Non-commutative Burkholder/Rosenthal inequalities. Preprint
22. p-spaces and applications. In preparation
23. p-spaces associated with an arbitrary von Neumann algebra. In: "Algèbres d'opérateurs et leurs applications en physique mathématique". 175-184, Colloque Internat. CNRS, Marseille 1977
24. Kadison, R.V., Ringrose, J.R.: Fundamentals of the theory of operator algebras, Volume II. Graduate Studies in Math. 16, AMS, 1997
25. Kaimanovich, V.: Measure-theoretic boundaries of Markov chains, 0 - 2 laws and entropy. In: Picardello, M.A., (ed) Proceedings of the Conference on Harmonic Analysis and Discrete Potential Theory. (Frascati 1991), Plenum 1992. pp 145-180
26. p-spaces. J. Funct. Anal. 56, 29-78 (1984)
27. Kümmerer, B.: A non-commutative individual theorem. Invent. Math. 46, 139-145 (1978)
28. Lance, E.C.: Ergodic theorems for convex sets and operator algebras. Invent. Math. 37, 201-214 (1975)
29. Nelson, E.: Notes on non-commutative integration. J. Funct. Anal. 15, 29-78 (1974)
30. Neveu, J.: Bases mathématiques du calcul des probabilités. Masson, 1970
31. Nevo. A.: Harmonic analysis and pointwise ergodic theorems for noncommuting transformations. J. Amer. Math. Soc. 7, (1994) 875-902
32. Nevo, A., Stein, E.M.: A generalisation of Birkoff's pointwise ergodic theorem. Acta Math. 173, 135-154 (1994)
33. Paschke, W.L.: Inner product modules over B*-algebras. Trans. Amer. Math. Soc. 182, 443-468 (1973)
34. p-spaces and completely p-summing maps. Astérisque. 247, 1998
35. Revuz, D.: Markov chains. North-Holland, 1984
36. Rota, G.-C.: An "alternierende verfahren" for general positive operators. Bull. A. M. S. 68, 95-102 (1962)
37. Sauvageot, J-L.: A note on almost uniform convergence in von Neumann algebras. In: "Quantum probability and related topics". Word Sc. Publ., 1991, pp 385-390
38. Sauvageot, J-L.: Markov quantum semigroups admit covariant Markov C*-dilations. Commun. Math. Phys. 106, 91-103 (1986)
39. Segal, I.E.: A noncommutative extension of abstract integration. Annals of Math. 57, 401-457, 595-596 (1953)
40. Stein, E.M.: On the maximal ergodic theorem. Proc. Nat. Acad. Sci. U.S.A. 47, 1894-1897 (1961)
41. Takesaki, M.: Conditional expectations in von Neumann algebras. J. Funct. Anal. 9, 306-321 (1972)
42. Takesaki, M.: Theory of operator algebras II. Encyclopaedia of mathematical sciences, 125. Operator algebras and non-commutative geometry. 6, Springer-Verlag, Berlin. 2003
43. Terp, M.: Interpolation between a von Neumann algebra and its predual. J. Operator Theory, 8, 327-360 (1982)
44. Voiculescu, D.: Symmetries of some reduced free product C*-algebras. In: "Operator algebras and their connections with topology and ergodic theory". 556-588. Lecture Notes in Math. 1132, Springer-Verlag, 1985
45. Walker, T.E.: Ergodic theorems for free group actions on von Neumann algebras. J. Funct. Anal. 150, 27-47 (1997)
46. Yeadon, F.J.: Ergodic theorems for semi-finite von Neumann algebras I. J. London Math. Soc. 16, 326-332 (1977)