The Mirror Property of Metric 2-Projection / Borodin P.A. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. ? 2. P. 31-36. [Moscow Univ. Math. Bulletin. Vol. 66, No 2, 2011.].

The concept of a mirror selection of a metric 2-projection is introduced (the metric 2-projection of two elements x₁, x₂ of a Banach space onto its subspace Y consists of all elements y∈Y such that the length of the broken line x₁yx₂ is minimal). It is proved that the existence of the mirror selection of a metric 2-projection onto eny 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.

Key words: metric 2-projection, Hilbert space, central mapping.