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

• Date: 1996
• Main Authors: Zagoroclnyuk, A. V., Загороднюк, А. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1996
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5218
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.