International Journal of Nonlinear Analysis and Applications
Character amenability of real Banach algebras
Document Type : Research Paper
Authors
Arak University
Abstract
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) $\varphi$-menability 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.
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