IJPAM: Volume 14, No. 1 (2004)

ON THE INFINITE-DIMENSIONAL HOLOMORPHIC
STRUCTURE ON TOPOLOGICAL BUNDLES
WITH FIBERS ISOMORPHIC TO ${\bf {C}}^{({\bf {N}})}$

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


Abstract.Let $(X,d)$ be a complete metrizable space and $E$ a suitable topological vector bundle on $X$ with fibers isomorphic to ${\bf {C}}^{({\bf {N}})}$. Here we show how to give a continuous and injective map $j: X \to V$, $V$ a complex Banach space, such that $j(X)$ is the zero-locus of a family of holomorphic functions on $V$ and the bundle $E$ has a holomorphic structure with respect to the complex analytic structure on $X$ induced by $j$.

Received: March 22, 2004

AMS Subject Classification: 32K05, 32L05

Key Words and Phrases: Banach analytic set, holomorphic vector bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 14
Issue: 1