Co-Isometric Weighted Composition Operators on Hilbert Spaces of Analytic Functions

被引：0
|
作者：
María J. Martín
Alejandro Mas
Dragan Vukotić
机构：
[1] Universidad de La Laguna,Departamento de Análisis Matemático
[2] Universidad Autónoma de Madrid,Departamento de Matemáticas
来源：
Results in Mathematics | 2020年 / 75卷
关键词：
Reproducing kernel; weighted Hardy spaces; weighted composition operator; unitary operator; co-isometric operator; 46E22; 47B33;
D O I：
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摘要：
We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns out to be equivalent to the property of being unitary. The result reveals a dichotomy identifying a specific family of weighted Hardy spaces as the only ones that support non-trivial operators of this kind.
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