Zeros of block-symmetric polynomials on Banach spaces
We investigate sets of zeros of block-symmetric polynomials on the direct sums of sequence spaces. Block-symmetric polynomials are more general objects than classical symmetric polynomials. An analogues of the Hilbert Nullstellensatz Theorem for block-symmetric polynomials on $\ell_p(\mathbb{C}^n)=\...
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Ivan Franko National University of Lviv
2020-06-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/32 |
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| author | V. Kravtsiv |
| author_facet | V. Kravtsiv |
| author_sort | V. Kravtsiv |
| collection | DOAJ |
| description | We investigate sets of zeros of block-symmetric polynomials on the direct sums of sequence spaces. Block-symmetric polynomials are more general objects than classical symmetric polynomials.
An analogues of the Hilbert Nullstellensatz Theorem for block-symmetric polynomials on $\ell_p(\mathbb{C}^n)=\ell_p \oplus \ldots \oplus \ell_p$ and $\ell_1 \oplus \ell_{\infty}$ is proved. Also, we show that if a polynomial $P$ has a block-symmetric zero set then it must be block-symmetric. |
| format | Article |
| id | doaj-art-a07863f363274693ab9de7d2b4bb36fa |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2020-06-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-a07863f363274693ab9de7d2b4bb36fa2025-08-20T03:33:14ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202020-06-0153220621110.30970/ms.53.2.206-21132Zeros of block-symmetric polynomials on Banach spacesV. Kravtsiv0Vasyl Stefanyk Precarpathian National UniversityWe investigate sets of zeros of block-symmetric polynomials on the direct sums of sequence spaces. Block-symmetric polynomials are more general objects than classical symmetric polynomials. An analogues of the Hilbert Nullstellensatz Theorem for block-symmetric polynomials on $\ell_p(\mathbb{C}^n)=\ell_p \oplus \ldots \oplus \ell_p$ and $\ell_1 \oplus \ell_{\infty}$ is proved. Also, we show that if a polynomial $P$ has a block-symmetric zero set then it must be block-symmetric.http://matstud.org.ua/ojs/index.php/matstud/article/view/32nullstellensatzblock-symmetric polynomialszero set of polynomials on banach spaces |
| spellingShingle | V. Kravtsiv Zeros of block-symmetric polynomials on Banach spaces Математичні Студії nullstellensatz block-symmetric polynomials zero set of polynomials on banach spaces |
| title | Zeros of block-symmetric polynomials on Banach spaces |
| title_full | Zeros of block-symmetric polynomials on Banach spaces |
| title_fullStr | Zeros of block-symmetric polynomials on Banach spaces |
| title_full_unstemmed | Zeros of block-symmetric polynomials on Banach spaces |
| title_short | Zeros of block-symmetric polynomials on Banach spaces |
| title_sort | zeros of block symmetric polynomials on banach spaces |
| topic | nullstellensatz block-symmetric polynomials zero set of polynomials on banach spaces |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/32 |
| work_keys_str_mv | AT vkravtsiv zerosofblocksymmetricpolynomialsonbanachspaces |