Abstract
We prove an analog of Hilbert's Nullstellensatz for ideals generated by a finite number of polynomial functionals on infinite-dimensional complex vector spaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
P. I. Bodnarchuk and V. Ya. Skorobagat'ko,Branched Continued Fractions and their Applications [in Russian], Naukova Dumka, Kiev (1974).
B. L. van der Waerden,Algebra, Springer, New York (1966).
A. V. Zagorodnyuk, “On two propositions of theScottish Book that apply to the rings of bounded polynomial functionals on Banach spaces,”Ukr. Mat, Zh.,48, No. 10, 1329–1336 (1996).
L. M. Druźkowski, “Two criteria for continuity of polynomials andG-holomorphic mappings in infinite dimensions,”Univ. Iagel. Acta Math.,24, 135–138 (1984).
R. D. Mauldin, ed.,The Scottish Book, BirkhÄuser, Boston (1981).
P. Mazet, “Une démonstration géométrique du Nullstellensatz analytique complexe,”Bull. Soc. Math. France,101, 287–301 (1982).
S. Mazur, and W. Orlicz, “Sur la divisibilité des polynÔmes abstraits,”C. R. Acad. Sci., Paris,202, 621–623 (1936).
J.-P. Ramis,Sous-ensembles analytiques d'une variété banachique complexe, Springer, Berlin (1970).
Additional information
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 13–20.
Rights and permissions
About this article
Cite this article
Zagorodnyuk, A.V. TheNulstellensatz on infinite-dimensional complex spaces. J Math Sci 96, 2951–2956 (1999). https://doi.org/10.1007/BF02169686
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02169686