Topological groups with finite von Neumann algebras of type I

Sbornik Mathematics

Volumn 196, Issue 3-4, 2005, Pages 447-463

  Shtern, A I ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

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[No Author keywords available]

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EID: 22544439329     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2005v196n03ABEH000887     Document Type: Article

References (80)

1. I. Kaplansky, "Groups with representations of bounded degree", Proc. Amer. Math. Soc. 1 (1950), 449-463.
2. S.A. Amitsur, "Groups with representations of bounded degree. II", Illinois J. Math. 5 (1961), 198-205.
3. I.M. Isaacs and D.S. Passman, "Groups with representations of bounded degree", Canad. J. Math. 16 (1964), 299-309.
4. E. Thoma, "Über unitäre Darstellungen abzählbarer, diskreter Gruppen", Math. Ann. 153 (1964), 111-138.
5. E. Thoma, "Eine Charakterisierung diskreter Gruppen vom Typ I", Invent. Math. 6 (1968), 190-196.
6. J. Dixmier, C*-algèbres et leurs représentations, 2nd ed., Gauthier-Villars, Paris 1969.
7. C.C. Moore, "Groups with finite dimensional irreducible representations", Trans. Amer. Math. Soc. 166 (1972), 401-410.
8. A.I. Stern (Shtern), "Locally bicompact groups with finite-dimensional irreducible representations", Mat. Sb. 90 (132):1 (1973), 86-93;
9. English transl. in Math. USSR-Sb. 19 (1974).
10. S. Grosser, R. Mosak, and M. Moskowitz, "Duality and harmonic analysis on central topological groups. I", Nederl. Akad. Wetensch. Proc. Ser. A 76 (1973), 65-77.
11. S. Grosser, R. Mosak, and M. Moskowitz, "Duality and harmonic analysis on central topological groups. II", Nederl. Akad. Wetensch. Proc. Ser. 76 (1973), 78-91;
12. S. Grosser, R. Mosak, and M. Moskowitz, "Correction to: Duality and harmonic analysis on central topological groups", Nederl. Akad. Wetensch. Proc. Ser. A 76 (1973), 375.
13. T.W. Palmer, "Classes of nonabelian, noncompact, locally compact groups", Rocky Mountain J. Math. 8 (1978), 683-741.
14. D. S. Passman, The algebraic structure of group rings, Wiley, New York 1977.
15. J. Ernest, "A new group algebra for locally compact groups", Amer. J. Math. 86 (1964), 467-492.
16. J. Ernest, "A new group algebra for locally compact groups. II", Canad. J. Math. 17 (1965), 604-615.
17. R. Eymard, "L'algèbre de Fourier d'un groupe localement compact", Bull. Soc. Math. France 92 (1964), 181-236.
18. W. Freedman and A. Ülger, "The Phillips properties", Proc. Amer. Math. Soc. 128 (2000), 2137-2145.
19. H. Maynard, "A geometric characterization of Banach spaces possessing the Radon-Nikodym property", Trans. Amer. Math. Soc. 185 (1973), 493-500.
20. I. Namioka and R. R. Phelps, "Banach spaces which are Asplund spaces", Duke Math. J. 42 (1975), 735-750.
21. C. Stegall, "The Radon-Nikodym property in conjugate Banach spaces. II", Trans. Amer. Math. Soc. 264 (1981), 507-519.
22. D. Yost, "Asplund spaces for beginners", Acta Univ. Carolin. Math. Phys. 34:2 (1993), 159-177.
23. G. Arsac, "Sur l'espace de Banach engendré par les coefficients d'une représentation unitaire", Publ. Dép. Math. (Lyon) 13:2 (1976), 1-101.
24. A. Bélanger and B.E. Forrest, "Geometric properties of some subspaces of VN(G)", Proc. Amer. Math. Soc. 122 (1994), 131-133;
25. "Geometric properties of coefficient function spaces determined by unitary representations of a locally compact group", J. Math. Anal. Appl. 193 (1995), 390-405.
26. L. J. Bunce, "The Dunford-Pettis property in the predual of a von Neumann algebra", Proc. Amer. Math. Soc. 116 (1992), 99-100.
27. C. H. Chu, "A note on scattered C*-algebras and the Radon-Nikodym property", J. London Math. Soc. (2) 24 (1981), 533-536.
28. C.H. Chu, B. Iochum, and S. Watanabe, "C*-algebras with the Dunford-Pettis property", Lecture Notes in Pure and Appl. Math., vol. 136, Springer-Verlag, Berlin 1992, pp. 67-70.
29. A. T.-M. Lau and A. Ülger, "Some geometric properties on the Fourier and Fourier-Stieltjes algebras of locally compact groups, Arens regularity and related problems", Trans. Amer. Math. Soc. 337 (1993), 321-359.
30. E.T. Ordman and S.A. Morris, "Almost locally invariant topological groups", J. London Math. Soc. (2) 9 (1974/75), 30-34.
31. M. Pahor, "The structure of certain group C*-algebras", Bull. Austral. Math. Soc. 47:1 (1993), 169-174.
32. I. Raeburn, "On group C*-algebras of bounded representation dimension", Trans. Amer. Math. Soc. 272 (1982), 629-644.
33. K. Taylor, "The type structure of the regular representation of a locally compact group", Math. Ann. 222:2 (1976), 211-214.
34. K. Taylor, "Geometry of the Fourier algebras and locally compact groups with atomic representations", Math. Ann. 262:2 (1983), 183-190.
35. G. Schlichting, "Polynomidentitäten und Darstellungen von Gruppen", Monatsh. Math. 90:4 (1980), 311-313.
36. G. Schlichting, Groups with representations of bounded degree, Lecture Notes in Math., vol. 706, Springer-Verlag, Berlin 1979.
37. D.S. Passman and W. V. Temple, "Groups with all irreducible modules of finite degree", Algebra (Moscow, 1998), de Gruyter, Berlin 2000, pp. 263-279.
38. S. Antonyan and M. Sanchis, "Extension of locally pseudocompact group actions", Ann. Mat. Pura Appl. (4) 181 (2002), 239-246.
39. A.V. Arhangel'skii, "On a theorem of W. W. Comfort and K.A. Ross", Comment. Math. Univ. Carolin. 40:1 (1999), 133-151.
40. A.V. Arhangel'skii, "Moscow spaces, Pestov-Tkačenko problem, and C-embeddings", Comment. Math. Univ. Carolin. 41 (2000), 585-595.
41. W. W. Comfort, T. Soundararajan, and F. J. Trigos-Arrieta, "Determining a weakly locally compact group topology by its system of closed subgroups", Papers in general topology and applications, New York Acad. Sci., New York 1994, pp. 25-33.
42. W. W. Comfort and F. J. Trigos-Arrieta, "Locally pseudocompact topological groups", Topology Appl. 62:3 (1995), 263-280.
43. D. Dikranjan and D. Shakhmatov, Algebraic structure of pseudocompact groups, Mem. Amer. Math. Soc., vol. 633, Amer. Math. Soc., Providence, RI 1998.
44. S. Hernandez and S. Macario, "Invariance of compactness for the Bohr topology", Topology Appl. 111:1-2 (2001), 161-173.
45. D. Remus and F. J. Trigos-Arrieta, "The Bohr topology of Moore groups", Topology Appl. 97:1-2 (1999), 85-98.
46. M. Sanchis, "Continuous functions on locally pseudocompact groups", Topology Appl. 86:1 (1998), 5-23.
47. M. G. Tkachenko, "On boundedness and pseudocompactness in topological groups", Mat. Zametki 41 (1987), 400-405;
48. English transl. in Math. Notes 41 (1987).
49. A. Weil, Sur les espaces à structure uniforme et sur la topologie générale, Hermann, Paris 1937.
50. A. I. Shtern, "Compact semitopological semigroups and reflexive representability of topological groups", Russian J. Math. Phys. 2:1 (1994), 131-132.
51. W. J. Davis, T. Figiel, W. B. Johnson, and A. Pelczynski, "Factoring weakly compact operators", J. Funct. Anal. 17 (1974), 311-327.
52. W. Banaszczyk, "On the existence of exotic Banach-Lie groups", Math. Ann. 264 (1983), 485-493.
53. W. Banaszczyk, Additive subgroups of topological vector spaces, Lecture Notes in Math., vol. 1466, Springer-Verlag, Berlin 1991.
54. W. Herer and J. P. R. Christensen, "On the existence of pathological submeasures and the construction of exotic topological groups", Math. Ann. 213 (1975), 203-210.
55. J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris 1969.
56. S. A. Gaal, Linear analysis and representation theory, Springer-Verlag, New York 1973.
57. M. A. Naimark and A.I. Stern (Shtern), Theory of group representations, Springer-Verlag, New York 1982.
58. R. Engelking, General topology, 2nd ed., Heldermann Verlag, Berlin 1989.
59. M. M. Day, Normed linear spaces, Springer-Verlag, New York 1973.
60. H.H. Schaefer, Topological vector spaces, 2nd ed., Springer-Verlag, New York-Berlin-Heidelberg 1999.
61. N. Dunford and J. T. Schwartz, Linear operators, vol, I, Interscience, London 1958.
62. R. E. Edwards, Functional analysis, theory and applications, Holt, Rinehart and Winston, New York 1965.
63. F. P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Reinhold, New York 1969.
64. E Hewitt and K. A. Ross, Abstract harmonic analysis, vol. I, Springer-Verlag, Berlin 1979.
65. A. Weil, L'intégration dans les groupes topologiques et ses applications, 2nd ed., Actualités Scientifiques et Industrielles, no. 1145, Hermann, Paris 1953.
66. R. Ellis, "Locally compact transformation groups", Duke Math. J. 24 (1957), 119-125.
67. I. Glicksberg, "Uniform boundedness for groups", Canad. J. Math. 14 (1962), 269-276.
68. N. Ya. Vilenkin, Editor's comments, Integration in topological groups and its applications, Inost. Lit., Moscow 1950, pp. 167-211. (Russian)
69. M. Enock and J.-M. Schwartz, Kac algebras and duality of locally compact groups, Springer-Verlag, Berlin 1992.
70. I. M. Gel'fand and D. A. Raǐkov, "Irreducible unitary representations of locally bicompact groups", Mat. Sb. 13(55) (1943), 301-316;
71. English transl. in Amer. Math. Soc. Transl. (2) 36.
72. A. I. Shtern, "Representations of topological groups in locally convex spaces: continuity properties and weak almost periodicity", Russian J. Math. Phys. 11:1 (2004), 81-108.
73. K. de Leeuw and L. Glicksberg, "Applications of almost periodic compactifications", Acta Math. 105 (1961), 63-97.
74. S. Sakai, C*-algebras and W*-algebras, Springer-Verlag Berlin 1971.
75. A. Joyal and R. Street, "An introduction to Tannaka duality and quantum groups", Category theory (Como, 1990), Lecture Notes in Math., vol. 1488, Springer-Verlag, Berlin 1991, pp. 413-492.
76. W. C. Waterhouse, "Dual groups of vector spaces", Pacific J. Math. 26:1 (1968), 193-196.
77. K. H. Hofmann and P. Mostert, Splitting in topological groups, Mem. Amer. Math. Soc. vol. 43, Amer. Math. Soc., Providence, RI 1963.
78. A. I. Shtern, "Criteria for weak and strong continuity of representations of topological groups in Banach spaces", Mat. Sb. 193:9 (2002), 139-156;
79. English transl. in Sb. Math. 193 (2002).
80. A.I. Shtern, "Continuity of Banach representations in terms of point variations", Russian J. Math. Phys. 9:2 (2002), 250-252.