Weak amenability of Beurling algebra free products
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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