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arXiv · 1404.2262

Amenable groups and bounded $Δ$-weak approximate identities

Mohammad Fozouni
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Abstract

Let $A$ be a Banach algebra with a non-empty character space. We say that a bounded net $\{e_α\}$ in $A$ is a bounded $Δ$-weak approximate identity for $A$ if, for each $a\in A$ and compact subset $K$ of $Δ(A)$, $||\widehat{e_αa}-\widehat{a}||_{K}=\sup_{ϕ\in K}|ϕ(e_αa)-ϕ(a)|\rightarrow 0$. For each $1<p<\infty$, we prove that the Figa-Talamanca Herz algebra, $A_{p}(G)$ has a bounded $Δ$-weak approximate identity if and only if $G$ is an amenable group. Also we give a sufficient condition for amenability of group $G$.

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Mohammad Fozouni. 2014-04-08. Amenable groups and bounded $Δ$-weak approximate identities. https://arxiv.org/abs/1404.2262

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