The Radon-Nikodym property for some Banach algebras related to the Fourier algebra
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- by Edmond E. Granirer
- Proc. Amer. Math. Soc. 139 (2011), 4377-4384
- DOI: https://doi.org/10.1090/S0002-9939-2011-10853-0
- Published electronically: April 22, 2011
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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 $G=\mathbb {R}^n$.References
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Bibliographic Information
- Edmond E. Granirer
- Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z4
- Email: granirer@math.ubc.ca
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 4377-4384
- MSC (2010): Primary 43A15, 46J10, 43A25, 46B22; Secondary 46J20, 43A30, 43A80, 22E30
- DOI: https://doi.org/10.1090/S0002-9939-2011-10853-0
- MathSciNet review: 2823083