International Journal of Nonlinear Analysis and Applications

Cohomological properties for certain Banach‎ ‎algebras on locally compact groups

Articles in Press

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

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 \(L_0^\infty(G)^*\).

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 09 November 2025
  • Receive Date: 09 June 2024
  • Revise Date: 13 November 2024
  • Accept Date: 19 November 2024