@article {
author = {Alimohammadi, Davood},
title = {Nonexpansive mappings on complex C*-algebras and their fixed points},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {7},
number = {1},
pages = {21-29},
year = {2016},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {},
doi = {10.22075/ijnaa.2015.289},
abstract = {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 $\mathsf{C}^*$-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.},
keywords = {Banach space,C*-algebra,Fixed point property,Nonexpansive mapping,normed linear space},
url = {https://ijnaa.semnan.ac.ir/article_289.html},
eprint = {https://ijnaa.semnan.ac.ir/article_289_75ca5b7bd96a777bf6f51352b152a680.pdf}
}