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

V. F. Gaposhkin


Abstract: 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.

UDC: 517.5

Received: 09.10.1969

 English version: Mathematical Notes, 1970, 8:5, 792–796

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