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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| Published in | Journal of mathematical analysis and applications Vol. 498; no. 2; p. 124984 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.06.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-247X 1096-0813 1096-0813 |
| DOI | 10.1016/j.jmaa.2021.124984 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 124984 |
| Author | Yakubovich, Dmitry Bello, Glenier Abadias, Luciano |
| Author_xml | – sequence: 1 givenname: Luciano surname: Abadias fullname: Abadias, Luciano email: labadias@unizar.es organization: Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spain – sequence: 2 givenname: Glenier surname: Bello fullname: Bello, Glenier email: glenier.bello@uam.es organization: Departamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain – sequence: 3 givenname: Dmitry surname: Yakubovich fullname: Yakubovich, Dmitry email: dmitry.yakubovich@uam.es organization: Departamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain |
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| Cites_doi | 10.1007/BF02392289 10.1090/S0002-9947-1987-0911086-8 10.1007/978-1-4419-6094-8 10.1007/s11785-018-0864-8 10.1112/S002461150501539X 10.7900/jot.2014jun06.2057 10.1007/BF01694057 10.1007/s11856-016-1417-3 10.1007/s11785-015-0501-8 10.1016/j.laa.2018.10.002 10.1007/BF01180596 10.4153/CMB-2017-058-4 10.1016/j.laa.2016.07.014 10.1090/S0002-9947-2010-05108-6 10.1016/j.laa.2014.03.020 10.1007/s00020-016-2298-x 10.4064/sm187-1-1 10.1090/proc/14736 10.1007/s00020-010-1801-z 10.1007/BF03651344 10.1090/S1061-0022-08-01013-3 10.1007/s11854-020-0085-8 10.1016/j.jmaa.2008.12.001 10.1016/j.jmaa.2016.10.065 10.1016/0022-1236(85)90037-0 10.4064/sm161-2-4 10.1016/j.jmaa.2015.01.067 10.1016/j.laa.2017.11.005 10.1007/s11785-018-0786-5 10.1007/s11856-011-0166-6 10.1016/j.jfa.2017.10.018 10.2307/1968732 10.1016/j.jfa.2017.10.008 10.1090/tran/7381 10.3906/mat-1403-41 10.2307/2159525 10.1007/s00020-003-1322-0 10.4064/sm156-1-1 10.1112/jlms.12199 10.2140/pjm.1951.1.133 10.7900/jot.2014jan29.2042 10.1002/sapm195938177 10.1007/978-1-4471-2170-1 10.1090/S0002-9947-02-03156-2 10.1016/j.laa.2018.09.022 10.1016/j.jmaa.2020.124035 10.1090/S0002-9947-1945-0012212-0 10.1007/s00020-012-2026-0 |
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