nonexpansive mappings on complex $mathsf{c}^star$--algebras and their fixed points

نویسندگان

davood alimohammadi

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}^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.

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عنوان ژورنال:
international journal of nonlinear analysis and applications

ناشر: semnan university

ISSN

دوره 7

شماره 1 2015

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