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The Type I Part of the Regular Representation

Published online by Cambridge University Press:  20 November 2018

Edward Formanek
Edward Formanek*
Affiliation:
Carleton University, Ottawa, Canada
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Let G be a discrete group and let H = L2(G), with norm | |. Let B(H) be the ring of bounded operators on H with the norm

The right regular representation of G on H induces an injection ρ : C[G] → B(H), and W(G) is the closure of the image of ρ in the weak operator topology on B(H) (C = complex numbers). Using ρ, we identify C[G] with its image in W(G).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1086 - 1089
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Amitsur, S. A. and Levitski, J., Minimal identities for algebras, Proc. Amer. Math. Soc. 1 (1950), 449–463.Google Scholar
2. Kaniuth, E., Der Typ der regulàren Darstellungen diskreter Gruppen, Math. Ann. 182 (1969), 334–339.Google Scholar
3. Smith, M., Regular representations, J. Functional Analysis 11 (1972), 401–406.Google Scholar
4. Sakai, S., C*-algebras and W*-algebras (Springer-Ver lag, New York, 1971).Google Scholar