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The mirror property of metric 2-projection. (English. Russian original) Zbl 1304.46023
Mosc. Univ. Math. Bull. 66, No. 2, 82-85 (2011); translation from Vest. Mosk. Univ. Mat. Mekh. 66, No. 2, 31-36 (2011).
Summary: The concept of a mirror selection of a metric 2-projection is introduced (the metric 2-projection of two elements \(x_{1}, x_{2}\) of a Banach space onto its subspace \(Y\) consists of all elements \(y\in Y\) such that the length of the broken line \(x_{1}yx_{2}\) is minimal). It is proved that the existence of the mirror selection of a metric 2-projection onto any subspace having a prescribed dimension or codimension is a characteristic property of a Hilbert space. A relation between the mirror selection of a metric 2-projection and the central selection of the usual metric projection is pointed out.
46C15 Characterizations of Hilbert spaces
54C65 Selections in general topology
46B20 Geometry and structure of normed linear spaces
Full Text: DOI
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