Ergodic properties for regular \(A\)-contractions
type: Item
instance of: scholarly article
title: Ergodic properties for regular \(A\)-contractions
zbMATH Open document ID: 1121.47005
author: Laurian Suciu
published in: Integral Equations and Operator Theory
publication date: 2006-11-07T00:00:00Z
review text: Let \(H\) be a complex Hilbert space and \(B(H)\) be the Banach algebra of all its bounded linear operators. An operator \(T\) in \(B(H)\) is called an \(A\)-contraction for a positive operator \(A\) in \(B(H)\) if \(T^* AT \leq A\); an \(A\)-contraction is called regular if \(AT = A^{1/2}TA^{1/2}\). In this paper, an orthogonal decomposition of \(H\) induced by a regular \(A\)-contraction is obtained and this is used to prove a certain version of the mean ergodic theorem and Patil's theorem. Some functional equations in the range of \(A^{1/2}\) are characterized analogously to the result of [\textit{M.\,Lin} and \textit{R.\,Sine}, J.~Oper.\ Theory 10, 153--166 (1983; Zbl 0553.47006)].
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 5071131
zbMATH Keywords: A-contraction
zbMATH Keywords: orthogonal decomposition
zbMATH Keywords: ergodic mean
reviewed by: Minping Qian
MaRDI profile type: Publication
full work available at URL: s00020-006-1417-5
OpenAlex ID: W2124898330
DOI: 10.1007/S00020-006-1417-5
description: scientific article; zbMATH DE number 5071131