Nearly invariant subspaces related to multiplication operators in Hilbert spaces of analytic functions
type: Item
instance of: scholarly article
title: Nearly invariant subspaces related to multiplication operators in Hilbert spaces of analytic functions
zbMATH Open document ID: 1079.47030
author: Christophe Erard
published in: Integral Equations and Operator Theory
publication date: 2005-02-24T00:00:00Z
review text: Let \({\mathcal H}\) be a Hilbert space of analytic functions defined on an open subset \({\mathcal W}\) of \({\mathbb C}^d\), stable under the multiplication operator \(M_u\) induced by some function \(u.\) Given a subspace \({\mathcal M}\) of \({\mathcal H}\) which is ``nearly invariant under division by \(u\)'', this paper provides a factorization linking each element of \({\mathcal M}\) to elements of \({\mathcal M}\ominus(M\cap M_u{\mathcal H})\) on the inverse image under \(u\) of a certain complex disc, for which a relatively simple formula is given. As its application, some interesting results involving an \(H^2\) control are also obtained, in particular, a factorization for the kernel of Toeplitz operators on Dirichlet spaces and a localization for the problem of extraneous zeros.
Mathematics Subject Classification ID: 47B32
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 32A60
zbMATH DE Number: 2138209
zbMATH Keywords: multiplication operators
zbMATH Keywords: nearly invariant subspaces
zbMATH Keywords: Hilbert space
reviewed by: Ze-Hua Zhou
MaRDI profile type: Publication
full work available at URL: s00020-003-1292-2
OpenAlex ID: W1975588766
DOI: 10.1007/S00020-003-1292-2
description: scientific article; zbMATH DE number 2138209