On two statements of “The scottish book” concerning a ring of bounded polynomial functionals on banach spaces - Zagoroclnyuk, A. V. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
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.