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Cohomological properties for certain Banach algebras on locally compact groups | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 18 آبان 1404 اصل مقاله (376.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34388.5137 | ||
| نویسنده | ||
| Seyedeh Somayeh Jafari | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| تاریخ دریافت: 20 خرداد 1403، تاریخ بازنگری: 23 آبان 1403، تاریخ پذیرش: 29 آبان 1403 | ||
| چکیده | ||
| For a locally compact group \(G\), let \(L_0^\infty(G)\) be the Banach space of all essentially bounded measurable functions on \(G\) vanishing at infinity. Here, we deal with a derivation problem for the Banach algebra \(L_0^\infty(G)^*\) equipped with a multiplication of Arens type. We first show that the Singer-Wermer conjecture for \(L_0^\infty(G)^*\) is valid only in the case where $G$ is abelian. Also, we characterize various cohomological properties for \(L_0^\infty(G)^*\) according to algebraic and topological properties of \(G\); in particular, we obtain diverse properties of \(G\) in terms of these notions based on derivations of \(L_0^\infty(G)^*\). | ||
| کلیدواژهها | ||
| Amenability؛ Banach algebra؛ derivation؛ essentially bounded measurable functions؛ locally compact group؛ vanishing at infinity | ||
| مراجع | ||
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