Operator inequalities, functional models and ergodicity

We discuss when an operator T, subject to a rather general inequality in hereditary form, admits a unitarily equivalent functional model of Agler type in the reproducing kernel Hilbert space associated to the inequality. The kernel need not be of Nevanlinna-Pick type. We define a defect operator D i...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 498; no. 2; p. 124984
Main Authors Abadias, Luciano, Bello, Glenier, Yakubovich, Dmitry
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2021
Subjects
Dilation
Ergodic properties
Functional model
Operator inequality
Dilation
Operator inequality
Ergodic properties
Functional model
Online AccessGet full text
ISSN0022-247X
1096-0813
DOI10.1016/j.jmaa.2021.124984

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Summary:We discuss when an operator T, subject to a rather general inequality in hereditary form, admits a unitarily equivalent functional model of Agler type in the reproducing kernel Hilbert space associated to the inequality. The kernel need not be of Nevanlinna-Pick type. We define a defect operator D in our context and discuss the structure of the spectrum of T when D is of finite rank. As a second application, some consequences concerning the ergodic behavior of the operator T are derived.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.124984