Inner multipliers of de Branges' spaces
type: Item
instance of: scholarly article
title: Inner multipliers of de Branges' spaces
zbMATH Open document ID: 0704.46037
DOI: 10.1007/BF01193757
author: Benjamin A. Lotto
published in: Integral Equations and Operator Theory
publication date: 1990-01-01T00:00:00Z
review text: The author considers the question of when an arbitrary \(H^{\infty}\) function m is a multiplier of the de Branges space \({\mathcal H}(b)\), where \(b\in unit\) ball of \(H^{\infty}\). Necessary and sufficient conditions that m be a multiplier of \({\mathcal H}(b)\) are obtained, and it is shown that there are no nonconstant inner multipliers of \({\mathcal H}(b)\), when b is a nonconstant extreme point of the unit ball of \(H^{\infty}\). The author provides a new proof of the known fact that \({\mathcal H}(b)\) is invariant under multiplication by z when b is not an extreme point of the unit ball of \(H^{\infty}\). Also, a new proof is given that an inner function m is a multiplier of \({\mathcal H}(b)\) for \(b(z)=(1+z)/2\) if and only if m belongs to the range of the Toeplitz operator \(T_{\overline{(1-z)/2}}\).
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 4155219
zbMATH Keywords: multiplier of the de Branges space
zbMATH Keywords: nonconstant inner multipliers
zbMATH Keywords: extreme point of the unit ball
zbMATH Keywords: range of the Toeplitz operator
reviewed by: Manfred Stoll
MaRDI profile type: Publication
cites work: Q5534423
cites work: On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
cites work: Q5727906
cites work: Q3752970
description: scientific article; zbMATH DE number 4155219