Lipschitz symmetric functions on Banach spaces with symmetric bases
We investigate Lipschitz symmetric functions on a Banach space $X$ with a symmetric basis. We consider power symmetric polynomials on $\ell_1$ and show that they are Lipschitz on the unbounded subset consisting of vectors $x\in \ell_1$ such that $|x_n|\le 1.$ Using functions $\max$ and $\min$ and tr...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2021-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/5568 |
| _version_ | 1797205791688622080 |
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| author | M.V. Martsinkiv S.I. Vasylyshyn T.V. Vasylyshyn A.V. Zagorodnyuk |
| author_facet | M.V. Martsinkiv S.I. Vasylyshyn T.V. Vasylyshyn A.V. Zagorodnyuk |
| author_sort | M.V. Martsinkiv |
| collection | DOAJ |
| description | We investigate Lipschitz symmetric functions on a Banach space $X$ with a symmetric basis. We consider power symmetric polynomials on $\ell_1$ and show that they are Lipschitz on the unbounded subset consisting of vectors $x\in \ell_1$ such that $|x_n|\le 1.$ Using functions $\max$ and $\min$ and tropical polynomials of several variables, we constructed a large family of Lipschitz symmetric functions on the Banach space $c_0$ which can be described as a semiring of compositions of tropical polynomials over $c_0$. |
| first_indexed | 2024-04-24T08:56:44Z |
| format | Article |
| id | doaj.art-75290c8eefbc49b6b41e6e1dd8acba6d |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:44Z |
| publishDate | 2021-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-75290c8eefbc49b6b41e6e1dd8acba6d2024-04-16T07:09:07ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102021-12-0113372773310.15330/cmp.13.3.727-7334812Lipschitz symmetric functions on Banach spaces with symmetric basesM.V. Martsinkiv0S.I. Vasylyshyn1T.V. Vasylyshyn2A.V. Zagorodnyuk3Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineVasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineVasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineVasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineWe investigate Lipschitz symmetric functions on a Banach space $X$ with a symmetric basis. We consider power symmetric polynomials on $\ell_1$ and show that they are Lipschitz on the unbounded subset consisting of vectors $x\in \ell_1$ such that $|x_n|\le 1.$ Using functions $\max$ and $\min$ and tropical polynomials of several variables, we constructed a large family of Lipschitz symmetric functions on the Banach space $c_0$ which can be described as a semiring of compositions of tropical polynomials over $c_0$.https://journals.pnu.edu.ua/index.php/cmp/article/view/5568lipschitz symmetric function on banach spacesymmetric basistropical polynomial |
| spellingShingle | M.V. Martsinkiv S.I. Vasylyshyn T.V. Vasylyshyn A.V. Zagorodnyuk Lipschitz symmetric functions on Banach spaces with symmetric bases Karpatsʹkì Matematičnì Publìkacìï lipschitz symmetric function on banach space symmetric basis tropical polynomial |
| title | Lipschitz symmetric functions on Banach spaces with symmetric bases |
| title_full | Lipschitz symmetric functions on Banach spaces with symmetric bases |
| title_fullStr | Lipschitz symmetric functions on Banach spaces with symmetric bases |
| title_full_unstemmed | Lipschitz symmetric functions on Banach spaces with symmetric bases |
| title_short | Lipschitz symmetric functions on Banach spaces with symmetric bases |
| title_sort | lipschitz symmetric functions on banach spaces with symmetric bases |
| topic | lipschitz symmetric function on banach space symmetric basis tropical polynomial |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/5568 |
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