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This article is cited in 1 scientific paper (total in 1 paper)
Lorentz sequence spaces
S. A. Rakov Kharkiv Civil Engineering Institute
Abstract:
It is shown that the condition
$$
\sup\limits_n\Bigl\{n^{1/2}\Bigl(\sum_{j\le n}c_j^2\Bigr)^{1/2}\Bigr/\sum_{j\le n}c_j\Bigr\}<\infty
$$
on the normalizing sequence $\{c_j\}_{j<\infty}$ of the Lorentz sequence space $\Lambda(c)$ is a necessary and sufficient condition for having each bounded linear operator acting from an arbitrary $\mathscr L_\infty$-space into $\Lambda(c)$ be 2-absolutely summing.
Received: 08.12.1974
Citation:
S. A. Rakov, “Lorentz sequence spaces”, Mat. Zametki, 20:4 (1976), 501–510; Math. Notes, 20:4 (1976), 837–842
Linking options:
https://www.mathnet.ru/eng/mzm7870 https://www.mathnet.ru/eng/mzm/v20/i4/p501
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Abstract page: | 220 | Full-text PDF : | 179 | First page: | 1 |
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