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An extension property for the Figà-Talamanca Herz algebra

Author(s): Christian Fiorillo
Journal: Proc. Amer. Math. Soc. 137 (2009), 1001-1011.
MSC (2000): Primary 43A07, 43A15, 43A22; Secondary 43A32, 43A45, 46J10
Posted: October 9, 2008
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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.

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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

DOI: 10.1090/S0002-9939-08-09679-2
PII: S 0002-9939(08)09679-2
Keywords: Amenable groups, Fig\`a-Talamanca Herz algebra, Fourier algebra, convolution operators.
Received by editor(s): March 5, 2008
Posted: October 9, 2008
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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