IJPAM: Volume 12, No. 1 (2004)

NON-EXTENDIBILITY OF CERTAIN HOLOMORPHIC
VECTOR BUNDLES ON INFINITE-DIMENSIONAL
DOMAINS

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


Abstract.As a sample we give the following result. Let $V$ be a complex locally convex, Hausdorff and Baire topological vector space such that its dual $V'$ is equipped with a Hausdorff and sequentially complete locally convex topology for which the natural pairing $V\times V'\to {\bf {C}}$ is continuous. Let $H$ be any closed hyperplane of $V'$. Fix any $P\in V$. There is a holomorphic vector bundle $E$ on $V\backslash \{P\}$ with fibers isomorphic to $H$ which is not the restriction of a holomorphic vector bundle on $V$ and such that for every open neighborhood $\Omega$ of $P$ in $V$ the holomorphic vector bundle $E\vert \Omega \cap U$ is not trivial.

Received: February 5, 2003

AMS Subject Classification: 32K05, 32L05

Key Words and Phrases: holomorphic vector bundle, infinite-dimensional complex manifold, Banach bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 1