Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 2025 11 09 Cohomological properties for certain Banach‎ ‎algebras on locally compact groups 10226 10.22075/ijnaa.2024.34388.5137 EN Seyedeh Somayeh Jafari Department of Mathematics, Payame Noor University, Tehran, Iran Journal Article 2024 06 09 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 \(L_0^\infty(G)^*\). Amenability‎ ‎Banach algebra‎ ‎Derivation‎ ‎essentially bounded measurable functions‎ ‎locally compact group‎ ‎vanishing at infinity https://ijnaa.semnan.ac.ir/article_10226_edfccb5cf44f7c2c385f8d4470117a0d.pdf