Let $ (A,\| \cdot \|) $ be a real Banach algebra. In this paper we first introduce left and right $\varphi$-amenability of $A$ and discuss the relation between left (right, respectively) $\varphi$-amenability and $\overline{\varphi}$-amenability of $A$ for $\varphi\in\triangle(A)\cup\{0\}$ where $\overline{\varphi}\in\triangle(A)$ is the conjugate of $\varphi$. Next we show that $A$ is left (right, respectively) $\varphi$-amenable if and only if $A_{\mathbb{C}}$ is left (right, respectively) $\varphi_{\mathbb{C}}$-amenable, where $A_{\mathbb{C}}$ is a suitable complexification of $ A $ and $\varphi_{\mathbb{C}}\in\triangle(A_{\mathbb{C}})$ is the induced character by $\varphi$ on $A_{\mathbb{C}}$. In continue, we give a hereditary property for 0-amenability of $A$. We also study relations between the injectivity of Banach left $A$-modules and right $\varphi$-amenability of $A$. Finally, we characterize the left character amenability of certain real Banach algebras.
Alihoseini, H., Alimohammadi, D. (2020). Character amenability of real Banach algebras. International Journal of Nonlinear Analysis and Applications, 11(2), 255-284. doi: 10.22075/ijnaa.2019.18915.2041
MLA
Hamidreza Alihoseini; Davood Alimohammadi. "Character amenability of real Banach algebras". International Journal of Nonlinear Analysis and Applications, 11, 2, 2020, 255-284. doi: 10.22075/ijnaa.2019.18915.2041
HARVARD
Alihoseini, H., Alimohammadi, D. (2020). 'Character amenability of real Banach algebras', International Journal of Nonlinear Analysis and Applications, 11(2), pp. 255-284. doi: 10.22075/ijnaa.2019.18915.2041
VANCOUVER
Alihoseini, H., Alimohammadi, D. Character amenability of real Banach algebras. International Journal of Nonlinear Analysis and Applications, 2020; 11(2): 255-284. doi: 10.22075/ijnaa.2019.18915.2041
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