Geodesic
Coefficient sequences in Hilbert and Banach space expansions
Izvestiya. Mathematics, Tome 5 (1971) no. 1, pp. 226-232 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article we prove some theorems about the sequences of coefficients which occur for expansions relative to a basis in a Banach space, and for a certain type of basis in $L_2[-\pi,\pi]$ investigated by K. I. Babenko, namely $\{|t|^\alpha e^{int}\}_{-\infty}^\infty$, $0\alpha1/2$. As an application of our results, we prove that there exists no universal basis in a separable Hilbert space. 
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     author = {N. I. Gurarii},
     title = {Coefficient sequences in {Hilbert} and {Banach} space expansions},
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}
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N. I. Gurarii. Coefficient sequences in Hilbert and Banach space expansions. Izvestiya. Mathematics, Tome 5 (1971) no. 1, pp. 226-232. http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a13/

[1] Altman M. Sh., “O bazisakh v prostranstve Gilberta”, Dokl. AN SSSR, 69 (1949), 483–485 | MR

[2] Babenko K. I., “O sopryazhennykh funktsiyakh”, Dokl. AN SSSR, 62 (1948), 157–160 | MR | Zbl

[3] Gelfand I. M., “Zamechanie k rabote N. K. Bari, Biortogonalnye sistemy i bazisy v gilbertovom prostranstve”, Uch. zap. MGU, 148 (1951), 224–225 | MR

[4] Gurarii V. I., Gurarii N. I., “O bazisakh v ravnomerno vypuklykh i ravnomerno gladkikh banakhovykh prostranstvakh”, Izv. AN SSSR. Ser. matem., 35 (1971), 210–215 | MR | Zbl