Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160101Nonexpansive mappings on complex C*-algebras and their fixed points212928910.22075/ijnaa.2015.289ENDavoodAlimohammadiDepartment of Mathematics, Faculty of Science, Arak university, Arak 38156-8-8349, Iran0000-0002-9398-6213Journal Article20150607A normed space $\mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E \longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $\mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (iii) $C_0 (X)$ does not have the fixed point property. We also show that if $A$ is a commutative complex $\mathsf{C}^*$-algebra with nonempty carrier space, then the following statements are equivalent: (i) Carrier space of $ A $ is infinite, (ii) $ A $ is infinite dimensional, (iii) $ A $ does not have the fixed point property. Moreover, we show that if $ A $ is an infinite complex $\mathsf{C}^*$-algebra (not necessarily commutative), then $ A $ does not have the fixed point property.https://ijnaa.semnan.ac.ir/article_289_75ca5b7bd96a777bf6f51352b152a680.pdf