Positive definite class functions on a topological group and characters of factor representations

Kyoto Journal of Mathematics

Volumn 45, Issue 2, 2005, Pages 355-379

  Hirai, Takeshi ^a   Hirai, Etsuko ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750057439     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250281995     Document Type: Article

References (15)

1. E. Bishop and K. de Leeuw, The representation of linear functionals by measures on sets of extreme points, Ann. Inst. Fourier 9 (1959), 305-331.
2. W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, de Gruyter Studies in Math. 20, 1995.
3. J. Dixmier, Von Neumann Algebras, North-Holland Mathmatical Library 27, 1981.
4. Les C-algèbres et leurs représentations, Gauthier-Villars Paris, 1964.
5. I. M. Gelfand and D. A. Raikov, Irreducible unitary representations of locally bicompact groups, Amer. Math. Transl. 36 (1964), 1-15 (Original Russian paper in Mat. Sbornik 13 (55) (1943), 301-315).
6. R. Godement, Théorie des caractères II, Definition et propriétés générales des caractès, Ann. Math. 59 (1954), 63-85.
7. [Halm] P. R. Halmos, Measure Theory, GTM 18, Springer-Verlag, 1988.
8. T. Hirai and E. Hirai, Character formula for wreath products of finite groups with the infinite symmetric group, in 'Proceedings of Japanese- German Seminar on Infinite Dimensional Harmanic Analysis, World Scientific, to appear.
9. Characters for the wreath products of compact groups with the infinite symmetric group, preprint.
10. T. Hirai, H. Shimomura, N. Tatsuuma and E. Hirai, Inductive limits of topologies, their direct products, and problems related to algebraic structures, J. Math. Kyoto Univ. 41 (2001), 475-505.
11. M. Krein, A ring of functions on a topological group, Doklady de l'Acad. des Sci. de 1'URSS 29 (1940), 275-280.
12. G. W. Mackey, Borel structure in groups and their duals, Tans. Amer. Math. Soc. 85 (1957), 134-165.
13. G. Pedersen, C-algebras and their automorphism groups, London Math. Soc. Monographs 14, Academic Press, 1979.
14. N. Tatsuuma, H. Shimomura and T. Hirai, On group topologies and unitary representations of inductive limits of topological groups and the case of the group of diffeomorphisms, J. Math. Kyoto Univ. 38 (1998), 551-578.
15. E. Thoma, Über unitäre Darstellungen abzählbarer, diskreter Gruppen, Math. Ann. 153 (1964), 111-138.