Geodesic
On finite-dimension Chebyshev subspaces of spaces with an integral metric
Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 361-380 Cet article a éte moissonné depuis la source Math-Net.Ru

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This is a detailed study of the problem of the existence and characterization of finite-dimensional Chebyshev subspaces of the spaces $\varphi(L)$ and $L^{p(t)}$ on the interval $I=[-1,1]$, where $\varphi(t)$ is an even nonnegative continuous nondecreasing function on the half-line $[0,+\infty)$, and the function $p(t)$ is measurable, finite, and positive almost everywhere on $I$. If $\varphi$ is an $N$-function, it is characterized as a Chebyshev subspace of the Orlicz spaces with the Luxemburg norm. 
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     title = {On finite-dimension {Chebyshev} subspaces of spaces with an integral metric},
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     url = {http://geodesic.mathdoc.fr/item/SM_1993_74_2_a4/}
}
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N. K. Rakhmetov. On finite-dimension Chebyshev subspaces of spaces with an integral metric. Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 361-380. http://geodesic.mathdoc.fr/item/SM_1993_74_2_a4/

[1] Matuszewska W., “On generalized Orlicz spaces”, Bull. Acad. Polon. Ser. math., 8:6 (1960), 349–353 | MR | Zbl

[2] Garkavi A. L., “Teorema suschestvovaniya elementa nailuchshego priblizheniya v prostranstvakh tipa $(F)$ s integralnoi metrikoi”, Matem. zametki, 8:5 (1970), 583–594 | MR | Zbl

[3] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR

[4] Akhiezer N. I., Krein M. G., O nekotorykh voprosakh teorii momentov, GONTI, Kharkov, 1938

[5] Kamuntavichyus D., “Kriterii suschestvovaniya konechnomernykh chebyshevskikh podprostranstv v prostranstve $L_\varphi$”, Litovskii matem. zhurnal, 30:1 (1990), 44–55 | MR | Zbl

[6] Jackson D., “A general class of problems in approximation”, Amer. J. Math., 46 (1924), 215–234 | DOI | MR | Zbl

[7] Hobby C. R., Rice J. R., “A moment problem in $L_1$-approximation”, Proc. Amer. Math. Soc., 16:4 (1965), 665–670 | DOI | MR | Zbl

[8] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, MGU, M., 1976 | MR

[9] Krasnoselskii M. A., Rutitskii Ya. B., Vypuklye funktsii i prostranstva Orlicha, GIFML, M., 1958

[10] Sharapudinov I. I., “O topologii prostranstva $\mathscr{L}^{p(t)}([0, 1])$”, Matem. zametki, 26:4 (1979), 613–632 | MR | Zbl

[11] Rakhmetov N. K., “O edinstvennosti elementa nailuchshego priblizheniya v nekotorykh funktsionalnykh prostranstvakh”, DAN SSSR, 316:3 (1991), 553–557 | MR | Zbl