IJPAM: Volume 7, No. 3 (2003)

CONTINUOUS HOMOGENEOUS POLYNOMIALS AND
ZERO-DIMENSIONAL ANALYTIC SUBSETS
OF INFINITE-DIMENSIONAL PROJECTIVE SPACES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $V$ be a locally convex and Hausdorff complex topological vector space and $Z$ a zero-dimensional closed analytic subscheme of ${\bf {P}}(V)$. Here we prove that the restriction map

\begin{displaymath}\rho _{Z,t}: H^0({\bf {P}}(V),\mathcal {O}_{{\bf {P}}(V)}(t)) \to
H^0(Z,\mathcal {O}_Z(t))\end{displaymath}

has dense image if and only if for every finite-dimensional linear subspace $W$ of $V$ the restriction map

\begin{displaymath}\rho _{Z\cap W,t;W}: H^0({\bf {P}}(W),\mathcal {O}_{{\bf {P}}(W)}(t)) \to
H^0(Z\cap W,\mathcal {O}_{Z\cap W}(t))\end{displaymath}

is surjective.

Received: May 14, 2003

AMS Subject Classification: 51E20

Key Words and Phrases: Hausdorff complex topological vector space, zero-dimensional closed analytic subscheme, finite-dimensional linear subspace

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 7
Issue: 3