On the amenability of a class of Banach algebras with application to measure algebra

Year, pages: 2019, 1177 - 1184

Let $\mathcal{L}$ be a Lau algebra and $X$ be a topologically invariant subspace of $\mathcal{L}^*$ containing $UC(\mathcal{L})$. We prove that if $\mathcal{L}$ has a bounded approximate identity, then strict inner amenability of $\mathcal{L}$ is equivalent to the existence of a strictly inner invariant mean on $X$. We also show that when ${\mathcal L}$ is inner amenable the cardinality of the set of topologically left invariant means on ${\mathcal L}^*$ is equal to the cardinality of the set of topologically left invariant means on $RUC(\mathcal{L})$. Applying this result, we prove that if $\mathcal{L}$ is inner amenable and $\langle {\mathcal{L}²}\rangle=\mathcal{L}$, then the essential left amenability of $\mathcal{L}$ is equivalent to the left amenability of $\mathcal{L}$. Finally, for a locally compact group $G$, we consider the measure algebra $M(G)$ to study strict inner amenability of $M(G)$ and its relation with inner amenability of $G$.

Ghanei, M., Nemati, M. 2019. On the amenability of a class of Banach algebras with application to measure algebra. In Mathematica Slovaca, vol. 69, no.5, pp. 1177-1184. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0299

Ghanei, M., Nemati, M. (2019). On the amenability of a class of Banach algebras with application to measure algebra. Mathematica Slovaca, 69(5), 1177-1184. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0299

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava