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Keywords:
$\rho $-orthogonality; left symmetric point; right symmetric point; space of continuous function; linear operator
$\rho $-orthogonality; left symmetric point; right symmetric point; space of continuous function; linear operator
Summary:
We study symmetric points with respect to $(\rho _+)$-orthogonality, $(\rho _{-})$-orthogonality and $\rho $-orthogonality in the space $C(K, \mathbb {X}),$ where $K$ is a perfectly normal, compact space and $ \mathbb X$ is a Banach space. We characterize left symmetric points and right symmetric points in $C(K, \mathbb {X})$ with respect to $(\rho _{+})$-orthogonality and $(\rho _{-})$-orthogonality, separately. Furthermore, we provide necessary conditions for left symmetric and right symmetric points with respect to $\rho $-orthogonality. As an application of these results we also study these symmetric points in the space of operators defined on some special Banach spaces.
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