Generalized multipliers for left-invertible analytic operators and its applications to commutant and reflexivity
Functional Analysis
2017-12-12 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1712.03794,
title = {Generalized multipliers for left-invertible analytic operators and its applications to commutant and reflexivity},
author = {Piotr Dymek and Artur Płaneta and Marek Ptak},
journal= {arXiv preprint arXiv:1712.03794},
year = {2017}
}
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23 pages