Some characterizations of the analytic Radon-Nikodým property in Banach spaces
type: Item
instance of: scholarly article
title: Some characterizations of the analytic Radon-Nikodým property in Banach spaces
zbMATH Open document ID: 0664.46016
DOI: 10.1016/0022-1236(88)90005-5
author: G. A. Edgar
author: P. N. Dowling
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: A Banach space X for which every bounded X-valued analytic function on the open unit disk has radial limits almost everywhere is said to have the analytic Radon-Nikodym property (aRNP). It is shown that X has aRNP if every operator from \(L^ 1\) to X which factors through \(L^ 1/H^ 1_ 0\) is representable, a characterization which is similar to that of RNP. Some immediate applications to properties of subspaces of \(L^ 1/H^ 1_ 0\) are indicated. The characterization also gives rise to a reasonable definition of aRNP for real spaces.
Mathematics Subject Classification ID: 46B22
zbMATH DE Number: 4086291
zbMATH Keywords: analytic Radon-Nikodym property
reviewed by: Ehrhard Behrends
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90005-5
OpenAlex ID: W2066623889
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description: scientific article; zbMATH DE number 4086291