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The amenability constant of the Fourier algebra

Author(s): Volker Runde
Journal: Proc. Amer. Math. Soc. 134 (2006), 1473-1481.
MSC (2000): Primary 46H20; Secondary 20B99, 22D05, 22D10, 43A40, 46J10, 46J40, 46L07, 47L25, 47L50
Posted: October 18, 2005
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Abstract: For a locally compact group $ G$, let $ A(G)$ denote its Fourier algebra and $ \hat{G}$ its dual object, i.e., the collection of equivalence classes of unitary representations of $ G$. We show that the amenability constant of $ A(G)$ is less than or equal to $ \sup \{ \deg(\pi) : \pi \in \hat{G} \}$ and that it is equal to one if and only if $ G$ is abelian.

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Additional Information:

Volker Runde
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: vrunde@ualberta.ca

DOI: 10.1090/S0002-9939-05-08164-5
PII: S 0002-9939(05)08164-5
Keywords: Locally compact group, Fourier algebra, amenable Banach algebra, amenability constant, almost abelian group, completely bounded map
Received by editor(s): September 27, 2004
Received by editor(s) in revised form: December 21, 2004
Posted: October 18, 2005
Additional Notes: This research was supported by NSERC under grant no. 227043-04
Communicated by: David R. Larson
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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