%0 Journal Article
%T Nonexpansive mappings on complex C*-algebras and their fixed points
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Alimohammadi, Davood
%D 2015
%\ 12/10/2015
%V 7
%N 1
%P 21-29
%! Nonexpansive mappings on complex C*-algebras and their fixed points
%K Banach space
%K C*-algebra
%K Fixed point property
%K Nonexpansive mapping
%K normed linear space
%R 10.22075/ijnaa.2015.289
%X A 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}^star$--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}^star$--algebra (not necessarily commutative), then $ A $ does not have the fixed point property.
%U https://ijnaa.semnan.ac.ir/article_289_75ca5b7bd96a777bf6f51352b152a680.pdf