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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1977, Volume 22, Issue 2, Pages 167–178 (Mi mz8038)

The $C$-convexity of Banach spaces with unconditional bases

S. A. Rakov

Abstract: A Banach space is called $C$-convex if the space $c_0$ cannot be represented finitely in it. Necessary and sufficient conditions for the $C$-convexity of a space with an unconditional basis and of the product of a space $Y$ with respect to the unconditional basis of a space $X$ are obtained. These conditions are rendered concrete for two classes of spaces: The Orlich space of sequences is $C$-convex if and only if its normalizing function satisfies the $\Delta_2$-condition; the Lorentz space of sequences is $C$-convex if and only if its normalizing sequence satisfies the condition $\varliminf\limits_{n\to\infty}\sum_{i=1}^{2n}c_i/\sum_{i=1}^nc_i=1$.

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English version:
Mathematical Notes, 1977, 22:2, 584–591

Bibliographic databases:

UDC: 513.3

Citation: S. A. Rakov, “The $C$-convexity of Banach spaces with unconditional bases”, Mat. Zametki, 22:2 (1977), 167–178; Math. Notes, 22:2 (1977), 584–591

Citation in format AMSBIB
\Bibitem{Rak77} \by S.~A.~Rakov \paper The $C$-convexity of Banach spaces with unconditional bases \jour Mat. Zametki \yr 1977 \vol 22 \issue 2 \pages 167--178 \mathnet{http://mi.mathnet.ru/mz8038} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=463891} \zmath{https://zbmath.org/?q=an:0358.46015} \transl \jour Math. Notes \yr 1977 \vol 22 \issue 2 \pages 584--591 \crossref{https://doi.org/10.1007/BF01780965}