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Nonexpansive mappings on complex C*-algebras and their fixed points | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 3، دوره 7، شماره 1، فروردین 2016، صفحه 21-29 اصل مقاله (383.5 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2015.289 | ||
| نویسنده | ||
| Davood Alimohammadi* | ||
| Department of Mathematics, Faculty of Science, Arak university, Arak 38156-8-8349, Iran | ||
| تاریخ دریافت: 17 خرداد 1394، تاریخ بازنگری: 10 مرداد 1394، تاریخ پذیرش: 14 شهریور 1394 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Banach space؛ C*-algebra؛ Fixed point property؛ Nonexpansive mapping؛ normed linear space | ||
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