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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| Format: | Article |
| Language: | deu |
| Published: |
Ivan Franko National University of Lviv
2020-06-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/32 |
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| Summary: | 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. |
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| ISSN: | 1027-4634 2411-0620 |