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Character amenability of real Banach algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 11، شماره 2، اسفند 2020، صفحه 255-284 اصل مقاله (218.74 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.18915.2041 | ||
| نویسندگان | ||
| Hamidreza Alihoseini؛ Davood Alimohammadi* | ||
| Arak University | ||
| تاریخ دریافت: 20 مهر 1398، تاریخ بازنگری: 27 آذر 1398، تاریخ پذیرش: 29 آذر 1398 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Banach algebra؛ Character amenable؛ Complexification؛ Banach left module؛ injectivity | ||
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