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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Radon-Nikodym property for some Banach algebras related to the Fourier algebra


Author: Edmond E. Granirer
Journal: Proc. Amer. Math. Soc. 139 (2011), 4377-4384
MSC (2010): Primary 43A15, 46J10, 43A25, 46B22; Secondary 46J20, 43A30, 43A80, 22E30
Published electronically: April 22, 2011
MathSciNet review: 2823083
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Abstract: The Radon-Nikodym property for the Banach algebras $ A_p^r(G)=A_p\cap L^r(G)$, where $ A_2(G)$ is the Fourier algebra, is investigated. A complete solution is given for amenable groups $ G$ if $ 1<p<\infty $ and for arbitrary $ G$ if $ p=2$ and $ A_2(G)$ has a multiplier bounded approximate identity. The results are new even for $ G=\mathbb{R}^n$.


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Additional Information

Edmond E. Granirer
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z4
Email: granirer@math.ubc.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10853-0
PII: S 0002-9939(2011)10853-0
Received by editor(s): November 15, 2009
Received by editor(s) in revised form: October 14, 2010, and October 20, 2010
Published electronically: April 22, 2011
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.