An extension property for the Figà-Talamanca Herz algebra
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Abstract:
Let $G$ be a locally compact group and $H$ a closed amenable subgroup of $G$. We prove that every element in $A_{p}(H)$ with compact support can be extended to an element of $A_{p}(G)$ of which we control the norm and support. The result is new even for the Fourier algebra. Our approach gives us new results concerning the operator norm closure of the convolution operators of $G$ with compact support.References
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Additional Information
- Christian Fiorillo
- Affiliation: Department of Mathematics, École Polytechnique Federale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland
- Address at time of publication: Via Pratocarasso 31, 6500 Bellinzona (TI), Switzerland
- Received by editor(s): March 5, 2008
- Published electronically: October 9, 2008
- Communicated by: Nigel J. Kalton
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1001-1011
- MSC (2000): Primary 43A07, 43A15, 43A22; Secondary 43A32, 43A45, 46J10
- DOI: https://doi.org/10.1090/S0002-9939-08-09679-2
- MathSciNet review: 2457440