Boundary behavior in Hilbert spaces of vector-valued analytic functions
type: Item
instance of: scholarly article
title: Boundary behavior in Hilbert spaces of vector-valued analytic functions
zbMATH Open document ID: 1127.46025
author: Marcus Carlsson
published in: Journal of Functional Analysis
publication date: 2007-06-26T00:00:00Z
review text: The author studies the boundary behavior of functions in Hilbert spaces of vector-valued analytic functions on the unit disc \(\mathbb D\). More specifically, the author gives operator-theoretic conditions on \(M_z\), where \(M_z\) denotes the operator of multiplication by the identity function on \(\mathbb D\), that imply that all functions in the space have non-tangential limits a.e., at least on some subset of the boundary. The main part of the article concerns the extension of a theorem by \textit{A.\,Aleman, S.\,Richter} and \textit{C.\,Sundberg} [Trans.\ Am.\ Math.\ Soc.\ 359, No.\,7, 3369--3407 (2007; Zbl 1126.47023)] to the case of vector-valued functions.
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46E20
zbMATH DE Number: 5167467
zbMATH Keywords: vector-valued analytic functions
zbMATH Keywords: non-tangential limits
zbMATH Keywords: invariant subspaces
zbMATH Keywords: index
reviewed by: Pengyan Hu
MaRDI profile type: Publication
full work available at URL: j.jfa.2007.02.006
OpenAlex ID: W2091906701
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DOI: 10.1016/J.JFA.2007.02.006
description: scientific article; zbMATH DE number 5167467