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. 72, N 2, 2017. P. 0].

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*∈*Y* such that the length of the broken line *x*_{1}*y**x*_{2} 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.