IJPAM: Volume 13, No. 3 (2004)

THE FACTORIALITY OF THE LOCAL RING OF
GERMS OF QUASI-ANALYTIC FUNCTIONS ON
A $p$-NORMED BANACH SPACE, $0 < p <1$

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


Abstract.Let $(V,\Vert \ \Vert )$ be a $p$-Banach space over $\mathbb {R}$ or $\mathbb {C}$ which is separated by its topological dual $V'$. Here we prove that the local ring of all germs at $0$ of quasi-analytic functions in a neighborhood of $0$ in $V$ is a unique factorization domain.

Received: March 7, 2004

AMS Subject Classification: 32K05

Key Words and Phrases: infinite-dimensional complex space, $p$-normed Banach space, Weierstrass Preparation Theorem, factorial ring, UFD

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 3