An extension property for the Figà-Talamanca Herz algebra

Fiorillo, Christian

doi:10.1090/S0002-9939-08-09679-2

An extension property for the Figà-Talamanca Herz algebra
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Proc. Amer. Math. Soc. 137 (2009), 1001-1011 Request permission

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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