Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$
For $n\geq 2,$ we show that every extreme point of the unit ball of ${\mathcal L}_s(^2l_{\infty}^n)$ is extreme in ${\mathcal L}_s(^2l_{\infty}^{n+1})$, which answers the question in [Period. Math. Hungar. 2018, 77 (2), 274-290]. As a corollary we show that every extreme point of the unit ball of ${...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2021-07-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4326 |
| Summary: | For $n\geq 2,$ we show that every extreme point of the unit ball of ${\mathcal L}_s(^2l_{\infty}^n)$ is extreme in ${\mathcal L}_s(^2l_{\infty}^{n+1})$, which answers the question in [Period. Math. Hungar. 2018, 77 (2), 274-290]. As a corollary we show that every extreme point of the unit ball of ${\mathcal L}_s(^2l_{\infty}^n)$ is extreme in ${\mathcal L}_s(^2l_{\infty})$. We also show that every extreme point of the unit ball of ${\mathcal P}(^2l_{\infty}^2)$ is extreme in ${\mathcal P}(^2l_{\infty}^n).$ As a corollary we show that every extreme point of the unit ball of ${\mathcal P}(^2l_{\infty}^2)$ is extreme in ${\mathcal P}(^2l_{\infty})$. |
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| ISSN: | 2075-9827 2313-0210 |