The order of approximation by partial sums of lacunary series in Banach spaces

Conditions are determined which must be imposed on an n_k lacunary sequence and a (C, 1)-basis in Banach. space in order that the analog of the theorem concerning best approximation by partial sums of lacunary trigonometrical series should hold.Translated from Matematicheskie Zametki, Vol. 8, No. 5, pp. 575–582, November, 1970.