Completions of matrices and the commutant lifting theorem
type: Item
instance of: scholarly article
title: Completions of matrices and the commutant lifting theorem
zbMATH Open document ID: 0786.47022
DOI: 10.1016/0022-1236(92)90002-Z
author: Dan Timotin
published in: Journal of Functional Analysis
publication date: 1992-07-23T00:00:00Z
review text: Some completion results for partially defined matrices with an infinite number of entries are obtained. These are then applied to obtain a description for the dilations of intertwining operators. In this context, a new proof of the commutant lifting theorem of Sz. Nagy and Foiaş [see \textit{C. Foiaş} and \textit{A. E. Frazho}, ``The commutant lifting approach to interpolation problems'' (1990; Zbl 0718.47010)] is given. A different approach which leads to a related description of the dilations of intertwining operators was also obtained from the theory of generalized Toeplitz kernels of Arocena and Cotlar [see \textit{R. Arocena}, Integral Equations Oper. Theory 6, 759-778 (1983; Zbl 0528.47013)].
reviewed by: Mircea I. Cîrnu
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 47A57
zbMATH DE Number: 39683
zbMATH Keywords: completion
zbMATH Keywords: partially defined matrices
zbMATH Keywords: dilations of intertwining operators
zbMATH Keywords: commutant lifting theorem
zbMATH Keywords: generalized Toeplitz kernels
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 39683