Acta Mathematica Sinica

, Volume 5, Issue 2, pp 165–169 | Cite as

Inner amenable groups and the inducedC*-algebra properties

  • Yuan Chuankuan


A discrete group can generate aC*-algebra, denoted byCβ*(G), by considering the so called conjugation regular representationβ of the groupG. Based on this treatment, the inner amenability ofG shall be characterized by the existence of the states onCβ* (G) satisfying some certain conditions.


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  1. [1]
    Akemann, C.A. and Walter, M.E., Unbounded negative definite functions,Can. J. Math.,13 (1981), 862–871.Google Scholar
  2. [2]
    Effros, E.G., Property Γ and inner amenability,Proc. Amer. Math. Soc.,47 (1975), 483–486.Google Scholar
  3. [3]
    Paschke, W.L., Inner amenability and conjugation operators,Proc. Amer. Math. Soc.,71 (1978), 117–118.Google Scholar
  4. [4]
    Pier, J.P., Quasi-invariance sur les localement compacts,Act. Math., Gauthier-Villars, 1982, Paris.Google Scholar
  5. [5]
    Pier, J.P., Amenable Locally Compact Groups, John Witley and Sons In., New York, 1984.Google Scholar
  6. [6]
    Yuan Chuankuan, The existence of inner invariant means onL (G),J. Math. Anal. Appl.,130 (1988), 514–524.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Yuan Chuankuan
    • 1
  1. 1.Department of Applied MathematicsTsing Hua UniversityChina

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