Weak amenability of Beurling algebra free products
Subject Areas : Statistics
Elham Gheisari
1
,
Akram Yousofzadeh
2
,
Mohammad Sadegh Asagri
3
1 - Department of Mathematics‎, ‎Faculty of Science‎, Central Tehran Branch‎, ‎Islamic Azad University‎,
2 - Department of Mathematics, Faculty of science, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Isfahan, Iran
3 - Department of Mathematics‎, ‎Faculty of Science‎, ‎Central Tehran Branch‎, ‎Islamic Azad University‎, Tehran‎, ‎Iran.
Keywords: وزن, میانگین‌پذیرضعیف, حاصلضرب آزاد, مشتق, گروه فشرده موضعی,
Abstract :
In this paper, for a discrete group $G=mathbb{Z}astmathbb{Z}_n$ and a weight function of polynomial$omega_alpha$, we show that the Burling algebra $ell^1(G, omega_alpha)$ is not weakly amenable and dihedral group $D_infty=mathbb{Z}_2astmathbb{Z}_2$ is amenable. We also show that for a continuous weight function $ omega$ under certain conditions on group $ G$, if the Burling algebra $ell^1(G, omega)$ is weakly amenable then $omega$ is bounded.In this paper, for a discrete group $G=mathbb{Z}astmathbb{Z}_n$ and a weight function of polynomial$omega_alpha$, we show that the Burling algebra $ell^1(G, omega_alpha)$ is not weakly amenable and dihedral group $D_infty=mathbb{Z}_2astmathbb{Z}_2$ is amenable. We also show that for a continuous weight function $ omega$ under certain conditions on group $ G$, if the Burling algebra $ell^1(G, omega)$ is weakly amenable then $omega$ is bounded.In this paper, for a discrete group $G=mathbb{Z}astmathbb{Z}_n$ and a weight function of polynomial$omega_alpha$, we show that the Burling algebra $ell^1(G, omega_alpha)$ is not weakly amenable and dihedral group $D_infty=mathbb{Z}_2astmathbb{Z}_2$ is amenable. We also show that for a continuous weight function $ omega$ under certain conditions on group $ G$, if the Burling algebra $ell^1(G, omega)$ is weakly amenable then $omega$ is bounded.
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