A new class of operators and a description of adjoints of composition operators
type: Item
instance of: scholarly article
title: A new class of operators and a description of adjoints of composition operators
zbMATH Open document ID: 1106.47023
author: Carl C. Cowen
author: Eva A. Gallardo Gutiérrez
published in: Journal of Functional Analysis
publication date: 2006-11-15T00:00:00Z
review text: Using the reproducing kernel of the standard Hardy Hilbert space \(H^2\), the authors establish first of all an explicit formula for the adjoint of a composition operator \(C_\varphi\) on \(H^2\), with \(\varphi\) an analytic self-map of the complex open unit disk (similarly for the classically weighted Bergman Hilbert spaces \({\mathcal A}_\alpha^2\), \(\alpha>-1\)). Then they introduce a general concept of so-called multiple-valued weighted composition operators on \(H^2\). Among other things, they show that, for a rational symbol \(\varphi\), the adjoint of \(C_\varphi\) can be expressed as a multiple-valued weighted composition operator.
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 46E22
zbMATH DE Number: 5072816
zbMATH Keywords: composition operator
zbMATH Keywords: adjoint of an operator
zbMATH Keywords: reproducing kernel
reviewed by: Hans Jarchow
MaRDI profile type: Publication
full work available at URL: j.jfa.2006.04.031
OpenAlex ID: W2038257216
cites work: The Commutant of an Analytic Toeplitz Operator
cites work: Linear fractional composition operators on \(H^ 2\)
cites work: Q4888816
cites work: Q4373534
cites work: Q5618011
cites work: Adjoints of linear fractional composition operators on the Dirichlet space
cites work: Adjoints of a class of composition operators
cites work: Q3196867
cites work: Composition operators and classical function theory
DOI: 10.1016/J.JFA.2006.04.031
description: scientific article; zbMATH DE number 5072816