Q913197
type: Item
instance of: scholarly article
title: Une caracterisation de la proprieté de Radon-Nikodym analytique pour les espaces de Banach isomorphes a leur carrés. (A characterization of the analytic Radon-Nikodym property for Banach spaces isomorphic to their squares)
zbMATH Open document ID: 0699.46012
DOI: 10.1007/BF01444537
author: Bouchta Khaoulani
author: Shangquan Bu
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164739
review text: We prove that if a complex Banach space isomorphic to its square fails the analytic Radon-Nikodym property, then there exists a bounded analytic regular and injective F: \({\mathbb{D}}\mapsto X\), there exists \(c>0\) and a sequence \((r_ n)_{n\geq 0}\) of radii strictly increasing to 1, such that \(\| F(re^{it})-F(r'e^{is})\| \geq c,\) for all \((t,s)\in [0,2\pi]^ 2,\) all \(r\leq r_ n\), all \(r'\geq r_{n+1}\), and all \(n\geq 0\). We obtain a new characterization of analytic Radon-Nikodym property in complex Banach spaces isomorphic to their square, by means of holomorphic embeddings of the open unit disk. This solves a problem of Aurich in these spaces.
Mathematics Subject Classification ID: 46B22
zbMATH DE Number: 4146836
zbMATH Keywords: complex Banach space isomorphic to its square
zbMATH Keywords: analytic Radon-Nikodym property
zbMATH Keywords: holomorphic embeddings of the open unit disk
reviewed by: Shangquan Bu
MaRDI profile type: Publication
cites work: Bounded holomorphic embeddings of the unit disk into Banach spaces
cites work: Q3796203
cites work: Deux remarques sur la propriété de Radon-Nikodym analytique
cites work: Boundary properties of analytic and harmonic functions with values in Banach space
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label: Une caracterisation de la proprieté de Radon-Nikodym analytique pour les espaces de Banach isomorphes a leur carrés. (A characterization of the analytic Radon-Nikodym property for Banach spaces isomorphic to their squares)
description: scientific article; zbMATH DE number 4146836