Derivations on the module extension Banach algebras

• Datum: 2021
• Hauptverfasser: Teymouri , A., Bodaghi , A., Ebrahimi Bagha, D., Bodaghi, A.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2021
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/240
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.986 We correct some results presented in [M. Eshaghi Gordji, F. Habibian, A. Rejali,  Ideal amenability of module extension Banach algebras, Int. J. Contemp. Math. Sci.,  2, No. 5, 213–219 (2007)] and, using the obtained consequences, we find necessary and sufficient conditions for the module extension $\mathcal A\oplus X$ to be $(\mathcal I\oplus Y)$-weakly amenable, where $\mathcal I$ is a closed ideal of the Banach algebra $\mathcal A$ and $Y$ is a closed $\mathcal A$-submodule of the Banach $\mathcal A$-bimodule $X.$ We apply this result to the module extension $\mathcal A\oplus(X_1\dotplus X_2),$ where $X_1,$ $X_2$ are two Banach $\mathcal A$-bimodules.