Iterates of a product of conditional expectation operators
type: Item
instance of: scholarly article
title: Iterates of a product of conditional expectation operators
zbMATH Open document ID: 1128.47011
author: Guy Cohen
published in: Journal of Functional Analysis
publication date: 2007-01-16T00:00:00Z
review text: Let \((\Omega ,{\mathcal F},\mu )\) be a probability space and let \(T=P_1 P_2 \dots P_d\) be a finite product of conditional expectations with respect to the sub \(\sigma\)-algebras \({\mathcal F}_1 ,{\mathcal F}_2 ,\dots,{\mathcal F}_d \). In the paper it is shown that for all \(f\in L_p(\mu)\), \(1\leq p\leq 2\), the sequence \(\{ T^n f\}\) converges \(\mu\)-a.e., with \[ \lim_{n\to \infty}T^n f=E[f| {\mathcal F}_1\cap {\mathcal F}_2 \cap \dots\cap {\mathcal F}_d ]\quad \mu\text{-a.e.} \]
reviewed by: Victor Sharapov
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47N30
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F25
zbMATH DE Number: 5116379
zbMATH Keywords: conditional expectations
zbMATH Keywords: maximal inequality
zbMATH Keywords: almost everywhere convergence
zbMATH Keywords: spectral sets
zbMATH Keywords: Cesàro summability
zbMATH Keywords: complex interpolation
MaRDI profile type: Publication
full work available at URL: j.jfa.2006.09.008
OpenAlex ID: W2018181108
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DOI: 10.1016/J.JFA.2006.09.008
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description: scientific article; zbMATH DE number 5116379