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The class of locally compact groups G for which C*(G) is amenable

Part of the Lecture Notes in Mathematics book series (LNM,volume 1359)

Keywords

  • Operator Algebra
  • Unitary Representation
  • Amenable Group
  • Projective Representation
  • Canonical Homomorphism

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Bibliography

  1. W.B. Arveson, "Subalgebras of C⋆-algebras", Acta Math. 123 (1969), 141–224.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. V. Bargmann, "On unitary ray representations of continuous groups," Ann. of Math. 59(1954), 1–46.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. C.J.K. Batty, "Semiperfect C⋆-algebras and the Stone-Weierstrass problem". J. London Math. Soc. 34(1986), 97–110.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. C. Chevalley, Théorie des groupes de Lie, Vol, 2, Groupes algébriques. Act. Sci. Ind. no 1152, Hermann, Paris, 1951

    MATH  Google Scholar 

  5. M.D. Choi and E.G. Effros, "Nuclear C⋆-algebras and the approximation property". Amer. J. Math. 100(1974), 61–79.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. M.D. Choi and E.G. Effros, "Separable nuclear C⋆-algebras and injectivity", Duke Math. J. 43(1976), 309–322.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. A. Connes, "Classification of injective factors", Ann. of Math. 103(1976), 73–115.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. A. Connes, "On the equivalence between injectivity and semidiscreteness for operator algebras", Collogues Internationaux C.M.R.S. No 274, 1977.

    Google Scholar 

  9. A. Connes, "On the cohomology of operator algebras", J. Functional Analysis 28 (1978), 248–253.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. M. Dang Ngoc, "Produits croisés restreints et extensions de groupes" Preprint.

    Google Scholar 

  11. J. Dixmier, "Sur la représentation régulière d'un groupe localement compact connexe", Ann. Sci. Ecole Norm. Sup. 3 (1970), 23–74.

    MathSciNet  Google Scholar 

  12. E.G. Effros and E.C. Lance, "Tensor products of operator algebras", Advances in Math. 25 (1977), 1–34.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. J.M.G. Fell, "A new proof that nilpotent groups are CCR", Proc. Amer. Math. Soc. 13 (1962), 93–99.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. J.M.G. Fell, "Weak containment and induced representations of groups", Canad. J. Math. 14 (1962), 237–268.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. R. Godement, "Theory of spherical functions, I", Trans. Amer. Math. Soc. 73 (1952), 496–556.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. P. Green, "The local structure of twisted covariance algebras", Acta Math. 140 (1978), 191–250.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. U. Haagerup, "All nuclear C⋆-algebras are amenable", Invent. Math. 74 (1983), 305–319.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Harish-Chandra "Representations of a semisimple Lie group on a Banach space I", Trans. Amer. Math. Soc. 75 (1953), 185–243.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. B.E. Johnson, "Cohomology in Banach Algebras", Mem. Amer. Math. Soc. 127 (1972).

    Google Scholar 

  20. A.A. Kirillov, "Elements of the Theory of Representations", Springer-Verlag, Berlin, 1976.

    CrossRef  MATH  Google Scholar 

  21. R. Lipsman, "Representation theory of almost connected groups", Pacific J. Math. 42 (1972), 453–467.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. V. Losert and H. Rindler, "Conjugation-invariant means." Preprint, 1986.

    Google Scholar 

  23. G.W. Mackey, "Unitary representations of group extensions I", Acta Math. 99 (1985), 265–311.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. D. Miličic, "Representations of almost connected groups." Proc. Amer. Math. Soc. 47 (1975), 517–518.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. A.L.T. Paterson, "Amenability" to appear, Monograph Series of the American Mathematical Society.

    Google Scholar 

  26. J.-P. Pier, "Amenable locally compact groups." John Wiley and Sons, New York, 1984.

    MATH  Google Scholar 

  27. L. Pukanszky, "Characters of connected Lie groups". Acta Math. 133 (1974), 81–137.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. M.A. Rieffel, "Unitary representations of group extensions; an algebraic approach to the Theory of Mackey and Blattner" Studies in Analysis, Advances in Mathematics, Supplementary Studies, Vol. 4 (1979), 43–81.

    MathSciNet  MATH  Google Scholar 

  29. J. Rosenberg, "Amenability of crossed products of C⋆-algebras", Comm. Math. Phys. 57 (1977), 187–191.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. J. Schwartz, "Two finite, non-hyperfinite, non-isomorphic factors" Comm. Pure Appl. Math. 16 (1963), 19–26.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. S. Wasserman, "Injective W⋆-algebras", Math. Proc. Cambridge Philos. Soc. 82 (1977), 39–47.

    CrossRef  MathSciNet  Google Scholar 

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© 1988 Springer-Verlag

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Paterson, A.L.T. (1988). The class of locally compact groups G for which C*(G) is amenable. In: Eymard, P., Pier, JP. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 1359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086603

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  • DOI: https://doi.org/10.1007/BFb0086603

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