The Lyapunov theorem on convexity and its use for sign-embeddings
It is proved (Theorem 1) that for a Banach space $X$ the following statements are equialent: i) the range of every $X$-valued $\sigma$-additive non-atomic measure of finite variation has convex closure; ii) $L_1$ does not sign-embed in $X$.
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8169 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |