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On isolated points in the dual spaces of locally compact groups

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References

  1. Bagget, L.: A separable group having a discrete dual space is compact. J. Funct. Analysis10, 1972

  2. Borel, A.: Density properties of certain subgroups of semisimple groups without compact factors. Ann. of Math.72, 179–188 (1960)

    Google Scholar 

  3. Celaroche, C., Krillov, A.: Sur les relations entre l'espace dual d'un groupe et la structure de ses sous-groupes fermés. Séminaire Bourbaki 343 (1967/68)

  4. Dixmier, J. D.: Points isolés dans le dual d'un groupe localement compact. Bull. Sc. Math.85, 91–96 (1961)

    Google Scholar 

  5. Dixmier, J. D.: LesC*-algèbres et leurs représentations. Paris: Gauthier-Villars 1964

    Google Scholar 

  6. Fell, J. M. G.: The dual spaces ofC*-algebras. Trans. of Amer. Soc.94, 365–400 (1960)

    Google Scholar 

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

    Google Scholar 

  8. Gelfand, I. M., Graev, M. I., Pyatetski-Shapiro, I. I.: Theory of representations and automorphic functions (Generalized functions, Vol. 6), 1966

  9. Harish-Chandra: Representations of semi-simple Lie groups, I, II, III. Trans. Amer. Math. Soc.75, 185–243 (1953);76, 26–65, 234–253 (1954)

    Google Scholar 

  10. Harish-Chandra: Representations of semi-simple Lie groups. IV. Amer. J. of Math.69, 564–628 (1956)

    Google Scholar 

  11. Howe, R.: Topological conditions on the dual of a group. Mathematisches Forschungsinstitut, Tagungsbericht 35, 1973

  12. Iwasawa, K.: On some types of topological groups. Ann. of Math.50, 507–558 (1949)

    Google Scholar 

  13. Kazhdan, D. A.: Connection of the dual space of a group with the structure of its closed subgroups. Functional Anal. i Priložen1, 71–74 (1967)

    Google Scholar 

  14. Mackey, G. W.: The theory of group representations. University of Chicago: Lecture notes 1955

  15. Mackey, G. W.: Induced representation of locally compact groups. I. Ann. of Math.55, 101–139 (1962)

    Google Scholar 

  16. Mackey, G. W.: Induced representations of groups and quantum mechanics. New York: W. A. Benjamin 1968

    Google Scholar 

  17. Selberg, A.: On discontinuous groups in higher dimensional symmetric spaces. Contribution to function theory. Bombay 147–164 (1960)

  18. Stern, A. I.: Separable locally compact groups with discrete support for the regular representation. Soviet Math. Dokl.12, 994–998 (1971)

    Google Scholar 

  19. Stern, A. I.: Connection between the topologies of a locally bicompact group and its dual space. Functional Analysis and its applications5, 311–317 (1971)

    Google Scholar 

  20. Wang, S. P.: Limit of lattices in a Lie group. Trans. of Amer. Soc.133, 519–526 (1968)

    Google Scholar 

  21. Wang, S. P.: On a theorem of representation of lattices. Proc. of Amer. Soc.23, 583–587 (1969)

    Google Scholar 

  22. Wang, S. P.: The dual space of semi-simple Lie groups. Amer. J. Math.23, 921–937 (1969)

    Google Scholar 

  23. Wang, S. P.: On density properties ofS-subgroups of locally compact groups. Ann. of Math.94 325–329 (1971)

    Google Scholar 

  24. Wang, S. P.: Homogeneous spaces with finite invariant volume. Amer. J. Math. (to appear)

  25. Wang, S. P.: On the first cohomology group of discrete groups with property (T). Proc. of Amer. Math. Soc.42, 621–624 (1974)

    Google Scholar 

  26. Whitney, H.: Elementary structure of real algebraic varieties. Ann. of Math.66, 545–556 (1967)

    Google Scholar 

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Partially supported by N.S.F. Grants GP 37688A1 and GP 7308571A2.

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Wang, P.S. On isolated points in the dual spaces of locally compact groups. Math. Ann. 218, 19–34 (1975). https://doi.org/10.1007/BF01350065

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  • DOI: https://doi.org/10.1007/BF01350065

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