Generalized multipliers for left-invertible analytic operators and its applications to commutant and reflexivity

We introduce generalized multipliers for left-invertible analytic operators. We show that they form a Banach algebra and characterize the commutant of such operators in its terms. In the special case, we describe the commutant of balanced weighted shift only in terms of its weights. In addition, we...

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Bibliographic Details
Published in:arXiv.org 2017-12
Main Authors: Dymek, Piotr, Płaneta, Artur, Ptak, Marek
Format: Article
Language:English
Subjects:
Banach spaces
Multipliers
Operators (mathematics)
Reflexivity
Online Access:Get full text
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Summary:We introduce generalized multipliers for left-invertible analytic operators. We show that they form a Banach algebra and characterize the commutant of such operators in its terms. In the special case, we describe the commutant of balanced weighted shift only in terms of its weights. In addition, we prove two independent criteria for reflexivity of weighted shifts on directed trees.
ISSN:2331-8422