Geodesic
Bases in uniformly convex and uniformly flattened Banach spaces
Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 220-225.

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The aim of this article is to obtain two-sided estimates for the norm of an element $x$ in a uniformly convex and uniformly flattened Banach space $E$ in terms of $l_p$-norms of the sequence of coefficients which occur in the expansion of $x$ in a basis $\{e_i\}^\infty_1$ . 
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V. I. Gurarii; N. I. Gurarii. Bases in uniformly convex and uniformly flattened Banach spaces. Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 220-225. http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a12/

[1] Grinblyum M. M., “Nekotorye teoremy o bazise v prostranstve tipa (V)”, Dokl. AN SSSR, 31 (1941), 428–432

[2] Gurevich L. A., “O bazise v sopryazhennom prostranstve”, Tr. seminara po funktsionalnomu analizu, t. 6, Voronezh, 1958, 42–43

[3] Day M. M., “Uniform convexity in factor and conjugate spaces”, Ann. of Math. (2), 45 (1944), 375–385 | DOI | MR | Zbl