A note on weighted Banach spaces of holomorphic functions
type: Item
instance of: scholarly article
title: A note on weighted Banach spaces of holomorphic functions
zbMATH Open document ID: 1047.46018
author: José Bonet
author: Elke Wolf
published in: Archiv der Mathematik
publication date: 2004-03-07T00:00:00Z
review text: The authors deal with weighted spaces of holomorphic functions. Let \(G\) be an open subset of \({\mathbb C}^N\) and \(v: G \to {\mathbb R}\) a continuous, strictly positive function, called a weight. Then the main result of the paper states that \[ (Hv)_0(G) = \{ f: G \to {\mathbb C} :\;f \text{ holomorphic, } v| f| \text{ vanishes at } \infty \} \] endowed with the weighted sup-norm \[ \| f\| _v = \sup_{z \in G } v(z) | f(z)| \] is always isomorphic to a subspace of \(c_0\). This was previously known only for very restricted classes of weights and open sets \(G\).
reviewed by: Wolfgang Lusky
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46B03
zbMATH DE Number: 2051650
zbMATH Keywords: spaces of holomorphic functions
zbMATH Keywords: weights
MaRDI profile type: Publication
full work available at URL: s00013-003-0568-8
OpenAlex ID: W2045711448
DOI: 10.1007/S00013-003-0568-8
description: scientific article; zbMATH DE number 2051650