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A cohomological characterization of amenable actions

Published online by Cambridge University Press:  24 October 2008

C. Anantharaman-Delaroche
Affiliation:
Université d'orléans, Département de Mathématiques et d'informatique, B.P. 6759, 45067 Orleans Cedex 2, France

Abstract

We give a new characterization of amenability for dynamical systems, in cohomological terms, which generalizes the classical characterization of amenable locally compact groups stated by Johnson.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Anantharaman-Delaroche, C.. Action moyennable d'un groupe localement compact surune algèbre de von Neumann. Math. Scand. 45 (1979), 289304.CrossRefGoogle Scholar
[2]Anantharaman-Delaroche, C.. Action moyennable d'un groupe localement compact surune algèbre de von Neumann. II. Math. Scand. 50 (1982), 251268.CrossRefGoogle Scholar
[3]Anantharaman-Delaroche, C.. Systèmes dynamiques non commutatifs et moyennabilité. Math. Ann. 279 (1987), 297315.CrossRefGoogle Scholar
[4]Anantharaman-Delaroche, C.. On relative amenability for von Neumann algebras. Compositio Math. 74 (1990), 333352.Google Scholar
[5]Connes, A.. On the cohomology of operator algebras. J. Fund. Anal. 28 (1978), 248253.CrossRefGoogle Scholar
[6]Guichardet, A.. Cohomologie des Groupes Topologiques el des Algèbres de Lie (Cedic, Fernand Nathan, 1980).Google Scholar
[7]Haagerup, U.. The standard form of von Neumann algebras. Math. Scand. 37 (1975), 271283.CrossRefGoogle Scholar
[8]Haagerup, U.. All nuclear C*-algebras are amenable. Invent. Math. 74 (1983), 305319.CrossRefGoogle Scholar
[9]Ionescu-Tulcea, A. and Ionescu-Tulcea, C.. Topics in the Theory of Liftings. Ergebnisse der Mathematik no. 48 (Springer-Verlag, 1969).CrossRefGoogle Scholar
[10]Johnson, B. E.. Cohomology of Banach Algebras. Memoirs Amer. Math. Soc. no. 127 (American Mathematical Society, 1972).CrossRefGoogle Scholar
[11]Kadison, R. V. and Ringrose, J. R.. Fundamentals of the Theory of Operator Algebras, vol. 2 (Academic Press, 1986).Google Scholar
[12]Paschke, W. L.. Inner product modules over B*-algebras. Trans. Amer. Math. Soc. 182 (1973), 443468.Google Scholar
[13]Roberts, J. E.. New light on the mathematical structure of algebraic field theory. Proc. Sympos. Pure Math. 38 (1982), 523550.CrossRefGoogle Scholar
[14]Sakai, S.. C*-algebras and W*-algebras. Ergebnisse der Mathematik no. 60 (Springer-Verlag, 1971).Google Scholar
[15]Schatten, R.. A Theory of Cross-Spaces. Ann. of Math. Studies no. 26 (Princeton University Press, 1950).Google Scholar
[16]Takesaki, M.. Theory of Operator Algebras, vol. 1 (Springer-Verlag, 1979).CrossRefGoogle Scholar
[17]Takesaki, M.. On the Hahn–Banach type theorem and the Jordan decomposition of module linear mapping over some operator algebras. Kōdai Math. Sent. Rep. 12 (1960), 110.Google Scholar
[18]Zimmer, R. J.. Amenable ergodic group actions and an application to Poisson boundaries of random walks. J. Fund. Anal. 27 (1978), 350372.CrossRefGoogle Scholar
[19]Zimmer, R. Z.. On the von Neumann algebra of an ergodic group action. Proc. Amer. Math. Soc. 66 (1977), 289293.CrossRefGoogle Scholar
[20]Zimmer, R. J.. Ergodic Theory of Semisimple Groups (Birkhäuser, 1984).CrossRefGoogle Scholar