Geodesic
Finite-codimensional Chebyshev subspaces in the complex space $C(Q)$
Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 178-191.

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We consider finite-codimensional Chebyshev subspaces in the complex space $C(Q)$, where $Q$ is a compact Hausdorff space, and prove analogs of some theorems established earlier for the real case by Garkavi and Brown (in particular, we characterize such subspaces). It is shown that if the real space $C(Q)$ contains finite-codimensional Chebyshev subspaces, then the same is true of the complex space $C(Q)$ (with the same $Q$). 
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     title = {Finite-codimensional {Chebyshev} subspaces in the complex space $C(Q)$},
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L. P. Vlasov. Finite-codimensional Chebyshev subspaces in the complex space $C(Q)$. Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 178-191. http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a2/

[1] Phelps R. R., “C̆ebys̆ev subspaces of finite codimension in $C(X)$”, Pacific J. Math., 13:2 (1963), 647–655 | MR | Zbl

[2] Garkavi A. L., “Zadacha Khelli i nailuchshee priblizhenie v prostranstve nepreryvnykh funktsii”, Izv. AN SSSR. Ser. matem., 31:3 (1967), 641–656 | MR | Zbl

[3] Garkavi A. L., “O kompaktakh, dopuskayuschikh chebyshevskie sistemy mer”, Matem. sb., 74 (116):2 (1967), 209–217 | MR | Zbl

[4] Brown A. L., “Chebyshev subspaces of finite codimension in spaces of continuous functions”, J. Austral. Math. Soc. Ser. A, 26:1 (1978), 99–109 | DOI | MR | Zbl

[5] Vlasov L. P., “Suschestvovanie elementov nailuchshego priblizheniya v kompleksnom $C(Q)$”, Matem. zametki, 40:5 (1986), 627–634 | MR | Zbl

[6] Danford N., Shvarts Dzh., Lineinye operatory. Obschaya teoriya, IL, M., 1962

[7] Singer I., Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, Berlin, 1970

[8] Vlasov L. P., “Approksimativnye svoistva podprostranstv konechnoi korazmernosti v $C(Q)$”, Matem. zametki, 28:2 (1980), 205–222 | MR | Zbl

[9] Vlasov L. P., “Edinstvennost obobschennykh elementov nailuchshego priblizheniya”, Matem. zametki, 25:2 (1979), 161–175 | MR | Zbl