Relaxation of metric constrained interpolation and a new lifting theorem
type: Item
instance of: scholarly article
title: Relaxation of metric constrained interpolation and a new lifting theorem
zbMATH Open document ID: 1060.47021
DOI: 10.1007/BF01193630
published in: Integral Equations and Operator Theory
publication date: 2002-01-01T00:00:00Z
review text: This long, very interesting paper is a natural continuation of the masterpiece [``Metric constrained interpolation, commutant lifting and systems'' (Oper. Theory, Adv. Appl. 100, Birkhäuser, Basel) (1998; Zbl 0923.47009)] that was written by \textit{I.~Gohberg} together with the authors of the present paper. In the present paper, the authors give an explicit solution to a new lifting interpolation problem that includes the commutant lifting theorem and some of its generalizations, such as the weighted commutant lifting of \textit{A. Biswas, C. Foias} and \textit{A. E. Frazho} [Acta Sci. Math. 65, 657--686 (1999; Zbl 0954.47018)] and the fixed point approach to Nehari's problem of \textit{S. Treil} and \textit{A. Volberg} [Oper. Theory, Adv. Appl. 71, 165--186 (1994; Zbl 0818.47026)]. The importance of this main result is shown by way of a number of applications to different variants of interpolation problems of Schur--Carathéodory, Nevanlinna--Pick, and Sarason's types, among others. Precise statements are too involved to be described in a short review; we simply recommend the reading of this paper to any operator theorist.
reviewed by: Pedro J. Paúl
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 20E05
zbMATH DE Number: 1760618
zbMATH Keywords: relaxed commutant lifting theorem
zbMATH Keywords: metric constrained interpolation
author: Ciprian Foias
author: Arthur E. Frazho
author: Marinus Kaashoek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1760618