Geodesic
Conditions for uniqueness of a~projector with unit norm
Matematičeskie zametki, Tome 22 (1977) no. 1, pp. 45-49.

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Suppose that in a normed linear space $B$ there exists a projector with unit norm onto a subspace $D$. A sufficient condition for this projector to be unique is the existence of a set $M\subset D^*$ which is total on $D$, each functional in which attains its norm on the unit sphere in $D$ and has a unique extension onto $B$ with preservation of norm. As corollaries to this fact, we obtain a series of sufficient conditions for uniqueness (some of which were previously known) as well as a necessary and sufficient condition for uniqueness. 
@article{MZM_1977_22_1_a4,
     author = {V. P. Odinets},
     title = {Conditions for uniqueness of a~projector with unit norm},
     journal = {Matemati\v{c}eskie zametki},
     pages = {45--49},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_1_a4/}
}
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V. P. Odinets. Conditions for uniqueness of a~projector with unit norm. Matematičeskie zametki, Tome 22 (1977) no. 1, pp. 45-49. http://geodesic.mathdoc.fr/item/MZM_1977_22_1_a4/