Normal extensions of subnormal composition operators
type: Item
instance of: scholarly article
title: Normal extensions of subnormal composition operators
zbMATH Open document ID: 0675.47012
published in: Michigan Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: For a \(\sigma\)-finite measure space \((X,\Sigma,m)\) and a measurable mapping \(T\) of \(X\) onto \(X\) the corresponding composition operator \(C\) on \(L^ 2(X,\Sigma,m)\) defined by \(Cf:=f\circ T\) is considered. If \(C\) is subnormal, the minimal normal extension of \(C\) is shown to be representable as a composition operator provided that \(T\Sigma\subseteq \Sigma\) and \(m\circ T^{-1}\) as well as \(m\circ T\) are mutually absolutely continuous with respect to \(m\). This is realized by the construction of a quasi-normal composition operator which extends \(C\) even without the additional properties of \(T\).
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 4105648
zbMATH Keywords: quasi-normal composition operator
author: Alan Lambert
reviewed by: Gerhard Garske
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003825
OpenAlex ID: W2085886205
DOI: 10.1307/MMJ/1029003825
description: scientific article; zbMATH DE number 4105648