Operator inequalities I. Models and ergodicity

2019/08/14 by Luciano Abadías, Abadias, Luciano, Glenier Bello-Burguet +3
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1908.05032

openalex publication_date 2019/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss when an operator, 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. To the contrary to the previous work, the kernel need not be of Nevanlinna-Pick type. We derive some consequences concerning the ergodic behavior of the operator.

Related

• Quantitative mean ergodic inequalities: power bounded operators acting on one single noncommutative L_p space
• An operator model in the annulus
• Operator-Valued Kernels, Machine Learning, and Dynamical Systems
• Ergodic behaviour of a Douglas-Rachford operator away from the origin
• Operator inequalities and characterizations