Zero sets of homogeneous polynomials containing infinite dimensional spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913433843138560 |
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| author | Aires, Mikaela Botelho, Geraldo |
| author_facet | Aires, Mikaela Botelho, Geraldo |
| contents | Let $X$ be a (real or complex) infinite dimensional linear space. We establish conditions on a homogeneous polynomial $P$ on $X$ so that, if $W$ is any finite dimensional subspace of $X$ on which $P$ vanishes, then $P$ vanishes on an infinite dimensional subspace of $X$ containing $W$. In the complex case, this is a step beyond the classical result due to Plichko and Zagorodnyuk. Applications to the real case are also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14241 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero sets of homogeneous polynomials containing infinite dimensional spaces Aires, Mikaela Botelho, Geraldo Functional Analysis 15A03, 46B87, 46G25, 47H60 Let $X$ be a (real or complex) infinite dimensional linear space. We establish conditions on a homogeneous polynomial $P$ on $X$ so that, if $W$ is any finite dimensional subspace of $X$ on which $P$ vanishes, then $P$ vanishes on an infinite dimensional subspace of $X$ containing $W$. In the complex case, this is a step beyond the classical result due to Plichko and Zagorodnyuk. Applications to the real case are also provided. |
| title | Zero sets of homogeneous polynomials containing infinite dimensional spaces |
| topic | Functional Analysis 15A03, 46B87, 46G25, 47H60 |
| url | https://arxiv.org/abs/2406.14241 |