Zeros of block-symmetric polynomials on Banach spaces

V. Kravtsiv

doi:10.30970/ms.53.2.206-211

V. Kravtsiv Vasyl Stefanyk Precarpathian National University

DOI: https://doi.org/10.30970/ms.53.2.206-211

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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