Geodesic
The mirror property of metric $2$-projection
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2011), pp. 32-36

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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. 
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     author = {P. A. Borodin},
     title = {The mirror property of metric $2$-projection},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {32--36},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_2_a4/}
}
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P. A. Borodin. The mirror property of metric $2$-projection. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2011), pp. 32-36. http://geodesic.mathdoc.fr/item/VMUMM_2011_2_a4/