Geodesic
Embedding Theorems in Group C*-Algebras†
Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 157-166

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a locally compact group and H an open subgroup of G. The embeddings of group C*-algebras associated with H into the group C*-algebras associated with G are studied. Three conditions for the embeddings given in terms of C*-norms of the group algebras, group representations and positive definite functions are shown to be equivalent. As corollary, we prove that the full C*-algebra of H can be embedded into the full C*-algebra of G in a natural way as well as the case for the reduced group C*-algebras. We also show that the embeddings hold for their duals and double duals.
DOI : 10.4153/CMB-1983-026-9
Mots-clés : Primary 22D25, secondary 43A65, 43A99, 47D35, Locally compact group, group representation, positive definite function, C*-algebra, von-Neumann algebra 
Lee, Tan-Yu. Embedding Theorems in Group C*-Algebras†. Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 157-166. doi: 10.4153/CMB-1983-026-9
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[1] 1. Akemann, C. A., Operator algebras associated with Fuchsian groups, Houston Journal of Math., 7 (3) 1981 295–301. Google Scholar

[2] 2. Akemann, C. A. and Lee, T.-Y., Some simple C*-algebras associated with free groups, Indiana Univ. Math. J., 29 (4) (1980), 505–511. Google Scholar

[3] 3. Akemann, C. A. and Ostrand, P. A., Computing norms in group C*-algebras, Amer. J. Math., 98 (4) (1976), 1015–1047. Google Scholar

[4] 4. Akemann, C. A. and Ostrand, P. A., On a tensor product C*-algebra associated with the free group on two generators, J. Math. Soc. Japan 27 (4) (1975), 589–599. Google Scholar

[5] 5. Choi, M. D., A simple C*-algebra generated by two finite-order unitaries, Canad. J. Math., 31 (1979), 867–880. Google Scholar

[6] 6. Choi, M. D., The full C*-algebra of the free group on two generators, Pac. J. Math., 87 (1) (1980), 41–47. Google Scholar

[7] 7. Choi, M. D. and Effros, E., Lifting problems and the cohomology of C*-algebras, Canad. J. Math., 29 (1977), 1092–1111. Google Scholar

[8] 8. Diximier, J., Les C*-algebras et leurs representations, Gauthier-Villars, Paris, 1969. Google Scholar

[9] 9. Ernest, J., A new group algebra for locally compact groups I, Amer. J. Math., 86 (1964), 467–492. Google Scholar

[10] 10. Eymard, P., L'alg?bre de Fourier d'un groupe localement compact. Bull. Soc. Math. France 92 (1964), 181–236. Google Scholar

[11] 11. Fell, J. M. G., Weak containment and induced representations of groups, Canad. J. Math. 14 (1962), 237–268. Google Scholar

[12] 12. Fell, J. M. G., The dual spaces of C*-algebras, Trans. Amer. Math. Soc. 94 (1960), 365–403. Google Scholar

[13] 13. Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis, I & II, Springer-Verlag, 1963 & 1970. Google Scholar

[14] 14. Mackey, G., The theory of group representation, Univ. of Chicago notes, 1955. Google Scholar

[15] 15. Pontryagin, L. S., Topological groups (translated by Arlen Brown), 2nd edition, Gordon and Breach Science Publishers, Inc., 1966. Google Scholar

[16] 16. Paschke, W. L. and Salinas, N., C*-algebras associated with free products of groups, Pac. J. Math., 82 (1979), 211–221. Google Scholar

[17] 17. Rickart, C., General Theory of Banach Algebras, Van Nostrand, New York, 1960. Google Scholar

[18] 18. Sakai, S., C*-algebras and W*-algebras, Springer-Verlag, 1971. Google Scholar

[19] 19. Tomiyama, J., On the projection of norm 1 in W*-algebra, Proc. Japan Acad. 33 (1957), 608–612. Google Scholar

[20] 20. Wassermann, S., On tensor products of certain group C*-algebras, J. Funct. Anal. 23 (1976), 238–254. Google Scholar

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