Embedding Theorems in Group C*-Algebras†
Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 157-166
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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.
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
@article{10_4153_CMB_1983_026_9,
author = {Lee, Tan-Yu},
title = {Embedding {Theorems} in {Group} {C*-Algebras{\textdagger}}},
journal = {Canadian mathematical bulletin},
pages = {157--166},
year = {1983},
volume = {26},
number = {2},
doi = {10.4153/CMB-1983-026-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-026-9/}
}
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