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Embedding Theorems in Group C*-Algebras†

Published online by Cambridge University Press:  20 November 2018

Tan-Yu Lee
Tan-Yu Lee*
Affiliation:
Department of Mathematics, University of Alabama University, AL 35486
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Abstract

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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.

Keywords

Primary 22D25secondary 43A6543A9947D35Locally compact groupgroup representationpositive definite functionC*-algebravon-Neumann algebra

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983, pp. 157 - 166
Copyright
Copyright © Canadian Mathematical Society 1983

Footnotes

†

This paper is essentially a generalization of some results in the author's Ph.D. thesis, written at the University of California, Santa Barbara, under the direction of Professor Charles A. Akemann.

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