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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.
MSC:
46C15 Characterizations of Hilbert spaces
54C65 Selections in general topology
46B20 Geometry and structure of normed linear spaces
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