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On two statements of “The scottish book” concerning a ring of bounded polynomial functionals on banach spaces

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Abstract

We prove an infinite-dimensional version of the Hilbert theorem about zeros (according to “The Scottish Book”). We study topological properties of the set of zeros of a continuous polynomial functional and establish necessary and sufficient conditions for this set to cut the space.

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Authors
  1. A. V. Zagorodnyuk
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Zagorodnyuk, A.V. On two statements of “The scottish book” concerning a ring of bounded polynomial functionals on banach spaces. Ukr Math J 48, 1507–1516 (1996). https://doi.org/10.1007/BF02377819

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  • DOI: https://doi.org/10.1007/BF02377819

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