Operator inequalities, functional models and ergodicity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:498

Article

Abadias, Luciano¹  Bello, Glenier^2,3  Yakubovich, Dmitry^2,3 

[1] Univ Zaragoza, Inst Univ Matemat & Aplicac, Dept Matemat, Zaragoza 50009, Spain

[2] Univ Autonoma Madrid, Dept Matemat, Madrid 28049, Spain

[3] CSIC UAM UC3M UCM, Inst Ciencias Matemat, Madrid, Spain

关键词: Dilation;    Functional model;    Operator inequality;    Ergodic properties;   

DOI  :  10.1016/j.jmaa.2021.124984

来源: Elsevier

【 摘 要 】

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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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