Zeros of block-symmetric polynomials on Banach spaces

  • V. Kravtsiv Vasyl Stefanyk Precarpathian National University
Keywords: Nullstellensatz, block-symmetric polynomials, zero set of polynomials on Banach spaces

Abstract

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.

Author Biography

V. Kravtsiv, Vasyl Stefanyk Precarpathian National University

Vasyl Stefanyk Precarpathian National University

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Published
2020-06-24
How to Cite
1.
Kravtsiv V. Zeros of block-symmetric polynomials on Banach spaces. Mat. Stud. [Internet]. 2020Jun.24 [cited 2020Jul.6];53(2):206-11. Available from: http://matstud.org.ua/ojs/index.php/matstud/article/view/32
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Articles