Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ C\sp{\ast} $-algebras generated by Fourier-Stieltjes transforms


Authors: Charles F. Dunkl and Donald E. Ramirez
Journal: Trans. Amer. Math. Soc. 164 (1972), 435-441
MSC: Primary 43A30; Secondary 22D25, 46L05
MathSciNet review: 0310548
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For G a locally compact group and $ \hat G$ its dual, let $ {\mathcal{M}_d}(\hat G)$ be the $ {C^ \ast }$-algebra generated by the Fourier-Stieltjes transforms of the discrete measures on G. We show that the canonical trace on $ {\mathcal{M}_d}(\hat G)$ is faithful if and only if G is amenable as a discrete group. We further show that if G is nondiscrete and amenable as a discrete group, then the only measures in $ {\mathcal{M}_d}(\hat G)$ are the discrete measures, and also the sup and lim sup norms are identical on $ {\mathcal{M}_d}(\hat G)$. These results are extensions of classical theorems on almost periodic functions on locally compact abelian groups.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A30, 22D25, 46L05

Retrieve articles in all journals with MSC: 43A30, 22D25, 46L05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0310548-3
PII: S 0002-9947(1972)0310548-3
Keywords: von Neumann mean, measure algebra, $ {C^ \ast }$-algebra, amenable, trace, dual of a locally compact group
Article copyright: © Copyright 1972 American Mathematical Society