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)

 

Some geometric properties on the Fourier and Fourier-Stieltjes algebras of locally compact groups, Arens regularity and related problems


Authors: Anthony To Ming Lau and Ali Ülger
Journal: Trans. Amer. Math. Soc. 337 (1993), 321-359
MSC: Primary 22D15; Secondary 22D25, 46H99, 46M05
MathSciNet review: 1147402
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a locally compact topological group and $ A(G)\;[B(G)]$ be, respectively, the Fourier and Fourier-Stieltjes algebras of $ G$. It is one of the purposes of this paper to investigate the $ {\text{RNP}}$ (= Radon-Nikodym property) and some other geometric properties such as weak $ RNP$, the Dunford-Pettis property and the Schur property on the algebras $ A(G)$ and $ B(G)$, and to relate these properties to the properties of the multiplication operator on the group $ {C^\ast}$-algebra $ {C^\ast}(G)$. We also investigate the problem of Arens regularity of the projective tensor products $ {C^\ast}(G)\hat \otimes A$, when $ B(G) = {C^\ast}{(G)^\ast}$ has the $ {\text{RNP}}$ and $ A$ is any $ {C^\ast}$-algebra. Some related problems on the measure algebra, the group algebra and the algebras $ {A_p}(G)$, $ P{F_p}(G)$, $ P{M_p}(G)\;(1 < p < \infty )$ are also discussed.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22D15, 22D25, 46H99, 46M05

Retrieve articles in all journals with MSC: 22D15, 22D25, 46H99, 46M05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1147402-7
PII: S 0002-9947(1993)1147402-7
Keywords: Locally compact groups, amenability, Fourier and Fourier-Stieltjes algebras, group algebra, measure algebra, group $ {C^\ast}$-algebra, multiplier algebra, regular representation, Arens regularity, Radon-Nikodym property, Dunford-Pettis property, Schur property
Article copyright: © Copyright 1993 American Mathematical Society