A Shimorin-type analytic model on an annulus for left-invertible operators and applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:477

Article

Pietrzycki, Pawel¹ 

[1] Uniwersytet Jagiellonski, Wydzial Matemat & Informat, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

关键词: Analytic model;    Multiplication operator;    Hilbert space of holomorphic functions;    Reproducing kernel Hilbert space;    Weighted composition operator;    Weighted shift on directed tree;   

DOI  :  10.1016/j.jmaa.2019.04.027

来源: Elsevier

【 摘 要 】

A new analytic model for left-invertible operators, which extends both Shimorin's analytic model for left-invertible and analytic operators and Gellar's model for bilateral weighted shift is introduced and investigated. We show that a left-invertible operator T, which satisfies certain conditions can be modeled as a multiplication operator M-z on a reproducing kernel Hilbert space of vector-valued analytic functions on an annulus or a disc. A similar result for composition operators in l(2)-spaces is established. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free