On a problem of topologies in infinite dimensional holomorphy
type: Item
instance of: scholarly article
title: On a problem of topologies in infinite dimensional holomorphy
zbMATH Open document ID: 0711.46032
DOI: 10.1007/BF01190669
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: In 1988, \textit{J. Taskinen} [Stud. Math. 91, No.1, 17-30 (1988; Zbl 0654.46060)] constructed a Fréchet-Montel space F such that F\({\hat \otimes}_{\pi}F\) contains \(\ell^ 1\). Therefore, this tensor product cannot be a Montel space. Using this space F and the representation of the space \(P(^ 2F)\) of the 2-homogeneous polynomials as a subspace of \(F'{\hat \otimes}_{\epsilon}F'\) it is shown that \(P(^ 2F)\) cannot be a Montel space too. As a consequence, the compact open topology and the Nachbin topology differ on each space H(U) of holomorphic functions on any open balanced subset U of F.
Mathematics Subject Classification ID: 46E50
Mathematics Subject Classification ID: 46G20
Mathematics Subject Classification ID: 46M05
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 4169424
zbMATH Keywords: Fréchet-Montel space
zbMATH Keywords: compact open topology
zbMATH Keywords: Nachbin topology
author: José M. Ansemil
author: J. Taskinen
reviewed by: Heinz Junek
MaRDI profile type: Publication
cites work: The compact open and the Nachbin ported topologies on spaces of holomorphic functions
cites work: Q3943468
cites work: A Banach-Dieudonné theorem for germs of holomorphic functions
cites work: The projective tensor product of Fréchet-Montel spaces
full work available at URL: https://doi.org/10.1007/bf01190669
OpenAlex ID: W2031670250
description: scientific article; zbMATH DE number 4169424