Complements to models for noncommuting operators
type: Item
instance of: scholarly article
title: Complements to models for noncommuting operators
zbMATH Open document ID: 0581.47007
DOI: 10.1016/0022-1236(84)90059-4
author: Arthur E. Frazho
published in: Journal of Functional Analysis
publication date: 1984-01-01T00:00:00Z
review text: This paper of A. E. Frazho develops a dilation theory for two noncommuting operators, which can in fact be extended to the n-operator case. This is accomplished by first extending the so-called Schäffer construction [cf. \textit{J. J. Schäffer}, Proc. Am. Math. Soc. 6, 322 (1955; Zbl 0064.116) or the book ''Harmonic analysis on operators on Hilbert space'' (1967; Zbl 0157.432) by \textit{B. Sz.-Nagy} and \textit{C. Foias}] for one operator to the Fock space setting. This is then combined with a new Wold decomposition to extend the Sz.-Nagy-Foias lifting theorem and also to extend the characteristic function theory. This work is related to work of \textit{J. W. Bunce} [viz., Models for N-tuples of noncommuting operators, J. Funct. Anal. 57, 21-30 (1984; Zbl 0558.47004)].
Mathematics Subject Classification ID: 47A45
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47L30
zbMATH DE Number: 3929749
zbMATH Keywords: dilation theory for two noncommuting operators
zbMATH Keywords: Schäffer construction
zbMATH Keywords: Fock space
zbMATH Keywords: Wold decomposition
zbMATH Keywords: Sz.-Nagy-Foias lifting theorem
zbMATH Keywords: characteristic function theory
reviewed by: Martin E. Walter
MaRDI profile type: Publication
full work available at URL: 0022-1236(84)90059-4
OpenAlex ID: W1998133878
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description: scientific article; zbMATH DE number 3929749