Let $\mathfrak{U}$ be a $\phi$-Johnson amenable Banach algebra where $\phi \in\Delta(\mathfrak{U})$ ($\Delta(\mathfrak{U})$ is the character space of $\mathfrak{U}$). Suppose that $X$ is a Banach $\mathfrak{U}$-bimodule such that $a.x=\phi(a)x$ for all $a\in \mathfrak{U}$, $x\in X$ or $x.a=\phi(a)x$ for all $a\in \mathfrak{U}$, $x\in X$. We show that any Lie derivation (not necessarily continuous) $\delta:\mathfrak{U}\rightarrow X$ with the property that $\mathfrak{S}(\delta)\subseteq \mathcal{Z}_{\mathfrak{U}}(X)$ ($\mathfrak{S}(\delta)$ is the separating space of $\delta$) can be decomposed into the sum of a continuous derivation and a center-valued trace.
Ghahramani,H. and Zamani,P. (2025). $\phi$-Johnson amenable Banach algebras and Lie derivations. (e5776). AUT Journal of Mathematics and Computing, (), e5776 doi: 10.22060/ajmc.2025.24052.1354
MLA
Ghahramani,H. , and Zamani,P. . "$\phi$-Johnson amenable Banach algebras and Lie derivations" .e5776 , AUT Journal of Mathematics and Computing, , , 2025, e5776. doi: 10.22060/ajmc.2025.24052.1354
HARVARD
Ghahramani H., Zamani P. (2025). '$\phi$-Johnson amenable Banach algebras and Lie derivations', AUT Journal of Mathematics and Computing, (), e5776. doi: 10.22060/ajmc.2025.24052.1354
CHICAGO
H. Ghahramani and P. Zamani, "$\phi$-Johnson amenable Banach algebras and Lie derivations," AUT Journal of Mathematics and Computing, (2025): e5776, doi: 10.22060/ajmc.2025.24052.1354
VANCOUVER
Ghahramani H., Zamani P. $\phi$-Johnson amenable Banach algebras and Lie derivations. AUT J Math Comput, 2025; (): e5776. doi: 10.22060/ajmc.2025.24052.1354
