Two classical theorems of function model theory in coordinate-free presentation

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Two classical theorems of function model theory in coordinate-free presentation. / Vasyunin, V. I.

In: Journal of Soviet Mathematics, Vol. 61, No. 2, 01.08.1992, p. 1951-1962.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c902dfa73daf4d7085864f00263bbe15,

title = "Two classical theorems of function model theory in coordinate-free presentation",

abstract = "This paper is devoted to the presentation, within the framework of a coordinate-free model, of two known Sz. Nagy-Foia{\c s} theorems: The first one deals with the correspondence between the invariant subspaces of a contraction T and the regular factorizations of its characteristic function θT, while the second one is the commutant lifting theorem. The proofs are based on a coordinate-free approach to the model. In the first theorem an essential point is the singling out of the role of functional imbeddings and the formulation of a criterion for the existence of an invariant subspace in terms of a functional imbedding of a special form. As far as the commutant lifting theorem is concerned, our approach enables us to give a parametrization of the lifted operators with the aid of one free parameter instead of two dependent ones, as done by Sz.-Nagy and Foia{\c s}.",

author = "Vasyunin, {V. I.}",

year = "1992",

month = aug,

day = "1",

doi = "10.1007/BF01095661",

language = "English",

volume = "61",

pages = "1951--1962",

journal = "Journal of Mathematical Sciences (Switzerland)",

issn = "1072-3374",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - Two classical theorems of function model theory in coordinate-free presentation

AU - Vasyunin, V. I.

PY - 1992/8/1

Y1 - 1992/8/1

N2 - This paper is devoted to the presentation, within the framework of a coordinate-free model, of two known Sz. Nagy-Foiaş theorems: The first one deals with the correspondence between the invariant subspaces of a contraction T and the regular factorizations of its characteristic function θT, while the second one is the commutant lifting theorem. The proofs are based on a coordinate-free approach to the model. In the first theorem an essential point is the singling out of the role of functional imbeddings and the formulation of a criterion for the existence of an invariant subspace in terms of a functional imbedding of a special form. As far as the commutant lifting theorem is concerned, our approach enables us to give a parametrization of the lifted operators with the aid of one free parameter instead of two dependent ones, as done by Sz.-Nagy and Foiaş.

AB - This paper is devoted to the presentation, within the framework of a coordinate-free model, of two known Sz. Nagy-Foiaş theorems: The first one deals with the correspondence between the invariant subspaces of a contraction T and the regular factorizations of its characteristic function θT, while the second one is the commutant lifting theorem. The proofs are based on a coordinate-free approach to the model. In the first theorem an essential point is the singling out of the role of functional imbeddings and the formulation of a criterion for the existence of an invariant subspace in terms of a functional imbedding of a special form. As far as the commutant lifting theorem is concerned, our approach enables us to give a parametrization of the lifted operators with the aid of one free parameter instead of two dependent ones, as done by Sz.-Nagy and Foiaş.

UR - http://www.scopus.com/inward/record.url?scp=34249839092&partnerID=8YFLogxK

U2 - 10.1007/BF01095661

DO - 10.1007/BF01095661

M3 - Article

AN - SCOPUS:34249839092

VL - 61

SP - 1951

EP - 1962

JO - Journal of Mathematical Sciences (Switzerland)

JF - Journal of Mathematical Sciences (Switzerland)

SN - 1072-3374

IS - 2

ER -

ID: 49880122