On Character Contractibility of Real Banach Algebras

Document Type : Research Paper

Authors
Davood Alimohammadi 1
Hammidreza Alihoseini 2
1 Department of Mathematics, Faculty of Science, Arak University, Arak 384817758, Iran
2 Department of Mathematics, Faculty of Science, Arak University
10.22075/ijnaa.2026.39992.5595
Abstract
‎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.
Keywords
Banach algebra
Character contractible
Complexification
Banach left module
projectivity&‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌lrm
Subjects
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International Journal of Nonlinear Analysis and Applications
Volume 17, Issue 8
August 2026
Pages 13-33

  • Receive Date 08 December 2025
  • Revise Date 03 March 2026
  • Accept Date 14 March 2026