The analogue of Bernstein’s inverse theorem for the one class of the space of sequences (in Ukrainian)

V. K. Maslyuchenko, H. A. Voloshyn
Chernivtsi National University, Chernivtsi, Ukraine
We introduce the space of numerical sequences $l_{\mathbf{p}}=\{{x=(\xi_{k})_{k=1}^{\infty}\colon} |x|=\sum\nolimits_{k=1}^{\infty}|{\xi_{k}}|^{p_k}\le+\infty\}$ with a quasi-norm $|\cdot|$ for an every sequence $\mathbf{p}=(p_k)_{k=1}^{\infty}$ of numbers $p_k$ from the interval $(0,1]$ and we prove the analogue of the inverse of Bernstein's theorem for this space.
inverse Bernstein’s theorem; quasi-norm; quasi-normed space; bounded balls; sequence of finite dimensional linear subspaces
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