Zeros of block-symmetric polynomials on Banach spaces

  • V. Kravtsiv Vasyl Stefanyk Precarpathian National University

Анотація

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.

Біографія автора

V. Kravtsiv, Vasyl Stefanyk Precarpathian National University

Vasyl Stefanyk Precarpathian National University

Посилання

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Опубліковано
2020-06-24
Як цитувати
Kravtsiv, V. (2020). Zeros of block-symmetric polynomials on Banach spaces. Математичні студії, 53(2), 206-211. https://doi.org/10.30970/ms.53.2.206-211
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