Coupling and relaxed commutant lifting

A.E. Frazho; S. ter Horst; M.A. Kaashoek

doi:10.1007/s00020-005-1365-5

Coupling and relaxed commutant lifting

A.E. Frazho, S. ter Horst, M.A. Kaashoek

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

A Redheffer type description of the set of all contractive solutions to the relaxed commutant lifting problem is given. The description involves a set of Schur class functions which is obtained by combining the method of isometric coupling with results on isometric realizations. For a number of special cases, including the case of the classical commutant lifting theorem, the description yields a proper parameterization of the set of all contractive solutions, but examples show that, in general, the Schur class function determining the contractive lifting does not have to be unique. Also some sufficient conditions are given guaranteeing that the corresponding relaxed commutant lifting problem has only one solution.

Original language	English
Pages (from-to)	33-67
Journal	Integral Equations and Operator Theory
Volume	54
Issue number	1
DOIs	https://doi.org/10.1007/s00020-005-1365-5
Publication status	Published - 2006

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MR2195229

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10.1007/s00020-005-1365-5

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title = "Coupling and relaxed commutant lifting",

abstract = "A Redheffer type description of the set of all contractive solutions to the relaxed commutant lifting problem is given. The description involves a set of Schur class functions which is obtained by combining the method of isometric coupling with results on isometric realizations. For a number of special cases, including the case of the classical commutant lifting theorem, the description yields a proper parameterization of the set of all contractive solutions, but examples show that, in general, the Schur class function determining the contractive lifting does not have to be unique. Also some sufficient conditions are given guaranteeing that the corresponding relaxed commutant lifting problem has only one solution.",

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AU - Kaashoek, M.A.

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AB - A Redheffer type description of the set of all contractive solutions to the relaxed commutant lifting problem is given. The description involves a set of Schur class functions which is obtained by combining the method of isometric coupling with results on isometric realizations. For a number of special cases, including the case of the classical commutant lifting theorem, the description yields a proper parameterization of the set of all contractive solutions, but examples show that, in general, the Schur class function determining the contractive lifting does not have to be unique. Also some sufficient conditions are given guaranteeing that the corresponding relaxed commutant lifting problem has only one solution.

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DO - 10.1007/s00020-005-1365-5

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EP - 67

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

ER -

Coupling and relaxed commutant lifting

Abstract

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