In this paper, we introduce and study $\varphi$-contractibility and character contractibility of real Banach algebras. We first show that if $ (A,\| \cdot \|) $ is a real Banach algebra with nonempty character space $\triangle(A)$ then $A$ is $\varphi$-contractibile if and only if $A$ is $\overline{\varphi}$-contractible, where $\varphi\in\triangle(A)$ and $\overline{\varphi}$ is the conjugate of $\varphi$. We next prove that if $ (A,\| \cdot \|) $ is a real Banach algebra and $A_{\mathbb{C}}$ is a suitable complexification of $ A $, then $A$ is character contractibile if and only if $A_{\mathbb{C}}$ is character contractibile. We also give a hereditary property for 0-contractibility of $A$. In continue, for a real Banach algebra $A$ we study relations between the projectivity of Banach left $A$-modules and left $\varphi$-contractibility of $A$. Finally, we investigate the left character contractibility of certain real Banach algebras.
Alimohammadi,D and Alihoseini,H . (2026). On Character Contractibility of Real Banach Algebras. International Journal of Nonlinear Analysis and Applications, 17(8), 13-33. doi: 10.22075/ijnaa.2026.39992.5595
MLA
Alimohammadi,D , and Alihoseini,H . "On Character Contractibility of Real Banach Algebras", International Journal of Nonlinear Analysis and Applications, 17, 8, 2026, 13-33. doi: 10.22075/ijnaa.2026.39992.5595
HARVARD
Alimohammadi D, Alihoseini H. (2026). 'On Character Contractibility of Real Banach Algebras', International Journal of Nonlinear Analysis and Applications, 17(8), pp. 13-33. doi: 10.22075/ijnaa.2026.39992.5595
CHICAGO
D Alimohammadi and H Alihoseini, "On Character Contractibility of Real Banach Algebras," International Journal of Nonlinear Analysis and Applications, 17 8 (2026): 13-33, doi: 10.22075/ijnaa.2026.39992.5595
VANCOUVER
Alimohammadi D, Alihoseini H. On Character Contractibility of Real Banach Algebras. IJNAA. 2026;17(8):13-33. doi: 10.22075/ijnaa.2026.39992.5595
International Journal of Nonlinear Analysis and Applications