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 ${...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vasyl Stefanyk Precarpathian National University
2021-07-01
|
| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4326 |
| _version_ | 1827281284973461504 |
|---|---|
| author | Sung Guen Kim |
| author_facet | Sung Guen Kim |
| author_sort | Sung Guen Kim |
| collection | DOAJ |
| description | 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 ${\mathcal P}(^2l_{\infty})$. |
| first_indexed | 2024-04-24T08:56:49Z |
| format | Article |
| id | doaj.art-8ab7d97a9b9e4ea48b10669bdbf26019 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:49Z |
| publishDate | 2021-07-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-8ab7d97a9b9e4ea48b10669bdbf260192024-04-16T07:07:42ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102021-07-0113228929710.15330/cmp.13.2.289-2973789Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$Sung Guen Kim0Kyungpook National University, 41566, Daegu, South KoreaFor $n\geq 2,$ 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 ${\mathcal P}(^2l_{\infty})$.https://journals.pnu.edu.ua/index.php/cmp/article/view/4326extreme pointsymmetric bilinear form2-homogeneous polynomials on $l_{\infty}$ |
| spellingShingle | Sung Guen Kim Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$ Karpatsʹkì Matematičnì Publìkacìï extreme point symmetric bilinear form 2-homogeneous polynomials on $l_{\infty}$ |
| title | Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$ |
| title_full | Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$ |
| title_fullStr | Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$ |
| title_full_unstemmed | Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$ |
| title_short | Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$ |
| title_sort | extreme points of mathcal l s 2l infty and mathcal p 2l infty |
| topic | extreme point symmetric bilinear form 2-homogeneous polynomials on $l_{\infty}$ |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/4326 |
| work_keys_str_mv | AT sungguenkim extremepointsofmathcalls2linftyandmathcalp2linfty |