Certain invariant subspace structure of analytic crossed products
type: Item
instance of: scholarly article
title: Certain invariant subspace structure of analytic crossed products
zbMATH Open document ID: 0642.46058
author: Tomomi Kominato
author: Kichi-Suke Saito
published in: Journal of the Mathematical Society of Japan
publication date: 1987-01-01T00:00:00Z
review text: In this note, we study the invariant subspace structure of analytic crossed products in the following setting. Let X be a standard Borel space with a \(\sigma\)-finite infinite positive measure \(\mu\), that is, \(\mu (X)=\infty\). Let \(\tau\) be an invertible measure preserving ergodic transformation on X. We consider the analytic crossed product \({\mathcal L}_+\) determined by \(L^{\infty}(X,\mu)\) and \(\tau\). Then we study the complete set of canonical models for Lat(\({\mathcal L}_+)\) which is the set of all left-pure left-invariant subspaces. Then we prove that there exists a left-pure, left-full, left-invariant subspace \({\mathcal M}_{\infty}\) such that, for every \({\mathcal M}\in Lat({\mathcal L}_+)\), there is a partial isometry V in \({\mathcal R}\) satisfying \({\mathcal M}_{\infty}=V{\mathcal M}\). If \(\mu\) is a finite measure, then we refer to \textit{M. AcAsey} [Pac. J. Math. 96, 457-473 (1981; Zbl 0424.46044)] and \textit{B. Solel} [ibid. 113, 201-214 (1984; Zbl 0586.46051)].
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 4046427
zbMATH Keywords: invariant subspace structure of analytic crossed products
zbMATH Keywords: invertible measure preserving ergodic transformation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/03940543
OpenAlex ID: W1994719488
DOI: 10.2969/JMSJ/03940543
description: scientific article; zbMATH DE number 4046427