Remarks on the interpolation and the similarity problem for nest subalgebras of von Neumann algebras
type: Item
instance of: scholarly article
title: Remarks on the interpolation and the similarity problem for nest subalgebras of von Neumann algebras
zbMATH Open document ID: 0830.46046
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-02-04T00:00:00Z
review text: Given a nest subalgebra of a von Neumann algebra \({\mathcal A}\) and vectors \(f\), \(g\) the author gives necessary and sufficient conditions for the existence of an operator \(A\) in \({\mathcal A}\) so that \(Af =g\). This generalizes a well-known theorem of E. C. Lance and the main result in \textit{M. Anoussis} [Proc. Am. Math. Soc. 114, No. 3, 707-710 (1992; Zbl 0780.47029)]; \textit{E. G. Katsoulis}, \textit{R. L. Moore} and \textit{T. T. Trent} [J. Oper. Theory 29, 115-123 (1993; Zbl 0813.47053)]. We also use the generalized Ringrose criterion to show that the similarity problem for continuous nests in certain crossed product factors of type III has a negative answer.
Mathematics Subject Classification ID: 46L10
Mathematics Subject Classification ID: 47L30
zbMATH DE Number: 762187
zbMATH Keywords: nest subalgebra of a von Neumann algebra
zbMATH Keywords: generalized Ringrose criterion
zbMATH Keywords: crossed product factors of type III
author: Elias G. Katsoulis
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1108
OpenAlex ID: W2093765411
DOI: 10.1006/JMAA.1995.1108
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description: scientific article; zbMATH DE number 762187