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 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.