Weighted shifts on directed trees. Their multiplier algebras, reflexivity and decompositions
Functional Analysis
2017-02-03 v1
Abstract
We study bounded weighted shifts on directed trees. We show that the set of multiplication operators associated with an injective weighted shift on a rooted directed tree coincides with the WOT/SOT closure of the set of polynomials of the weighted shift. From this fact we deduce reflexivity of those weighted shifts on rooted directed trees whose all path-induced spectral-like radii are positive. We show that weighted shifts with positive weights on rooted directed trees admit a Wold-type decomposition. We prove that the pairwise orthogonality of the factors in the decomposition is equivalent to the weighted shift being balanced.
Keywords
Cite
@article{arxiv.1702.00765,
title = {Weighted shifts on directed trees. Their multiplier algebras, reflexivity and decompositions},
author = {Piotr Budzynski and Piotr Dymek and Artur Planeta and Marek Ptak},
journal= {arXiv preprint arXiv:1702.00765},
year = {2017}
}