Geodesic
The operator of minimal continuance of linear functionals
Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 539-550.

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In terms of weak differentiability of norms and algebraic complementation of subspaces, the single-valuedness of the Hahn–Banach continuation is characterized, as well as its linearity as an operator. The connection is established between this continuation and the best approximation by the annihilator of the given subspace. 
@article{MZM_1977_21_4_a11,
     author = {P. K. Belobrov},
     title = {The operator of minimal continuance of linear functionals},
     journal = {Matemati\v{c}eskie zametki},
     pages = {539--550},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a11/}
}
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P. K. Belobrov. The operator of minimal continuance of linear functionals. Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 539-550. http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a11/