RUS  ENG
Full version
JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011 Number 2, Pages 32–36 (Mi vmumm670)

Mathematics

The mirror property of metric $2$-projection

P. A. Borodin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The notion of a mirror selection out of metric $2$-projection is introduced (metric $2$-projection of two elements $x_1$, $x_2$ of a Banach space onto its subspace $Y$ consists of all those elements $y\in Y$, for which the length of the broken line $x_1yx_2$ is minimal). It is proved that the existence of mirror selection out of metric $2$-projection onto every subspace having a prescribed dimension or codimemsion is a characteristic property of Hilbert space. A relation between mirror selection out of metric $2$-projection and central selection out of the usual metric projection is pointed out.

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

UDC: 517.982.256

Received: 28.04.2010


 English version:
Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2011, 66:2, 82–85

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025