Isomorphic operator algebras and conjugate inner functions
type: Item
instance of: scholarly article
title: Isomorphic operator algebras and conjugate inner functions
zbMATH Open document ID: 0771.47013
published in: Michigan Mathematical Journal
publication date: 1993-01-16T00:00:00Z
review text: Let \(D\) be the open unit disk of the complex plane and \(m\) the normalized arclength measure on \(\partial U\). If \(\varphi\) is a non constant inner function on \(D\), let \(C_ \varphi\in L(H^ 2)\) be the composition operator \(C_ \varphi(f)=f\circ\varphi\). If \(f\in H^ \infty\), let \(T_ f\) be the analytic Toeplitz operator \(T_ f\in L(H^ 2)\), \(T_ f(h)=fh\). Let \(A_ \varphi\) denote the norm closed algebra generated by \(C_ \varphi\) and \(\{T_ f\): \(f\in H^ \infty\}\). The main result is that, given \(\varphi\) and \(\psi\) nonconstant nonperiodic inner functions, then there exists an analytic homeomorphism \(\tau\) of \(D\) such that \(\tau\circ\psi=\varphi\circ\tau\) if and only if \(A_ \varphi\) and \(A_ \psi\) are isomorphic.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47L30
zbMATH DE Number: 93891
zbMATH Keywords: composition operator
zbMATH Keywords: analytic Toeplitz operator
zbMATH Keywords: nonperiodic inner functions
zbMATH Keywords: analytic homeomorphism
author: Thomas Hoover
reviewed by: Gustavo Corach
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004519
OpenAlex ID: W2062794166
DOI: 10.1307/MMJ/1029004519
description: scientific article; zbMATH DE number 93891