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Weak amenability of Beurling algebra free products | ||
| Journal of New Researches in Mathematics | ||
| مقاله 5، دوره 6، شماره 28، فروردین و اردیبهشت 2021، صفحه 45-56 اصل مقاله (2.13 M) | ||
| نوع مقاله: research paper | ||
| نویسندگان | ||
Elham Gheisari1؛ Akram Yousofzadeh 2؛ Mohammad Sadegh Asagri  3
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| 1Department of Mathematics‎, ‎Faculty of Science‎, Central Tehran Branch‎, ‎Islamic Azad University‎, | ||
| 2Department of Mathematics, Faculty of science, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Isfahan, Iran | ||
| 3Department of Mathematics‎, ‎Faculty of Science‎, ‎Central Tehran Branch‎, ‎Islamic Azad University‎, Tehran‎, ‎Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Derivative؛ weakly amenable؛ weight؛ locally compact group؛ free Product | ||
| مراجع | ||
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