Geodesic
Coefficient sequences in Hilbert and Banach space expansions
Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 226-232.

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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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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/

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