Unbounded subnormal weighted shifts on directed trees I
Functional Analysis
2013-10-15 v1
Abstract
A new method of verifying the subnormality of unbounded Hilbert space operators based on an approximation technique is proposed. Diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established. An approach to this issue via consistent systems of probability measures is invented. The role played by determinate Stieltjes moment sequences is elucidated. Lambert's characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi-analytic vectors, which is a new phenomenon in this area.
Cite
@article{arxiv.1203.0140,
title = {Unbounded subnormal weighted shifts on directed trees I},
author = {Piotr Budzyński and Zenon Jan Jabłoński and Il Bong Jung},
journal= {arXiv preprint arXiv:1203.0140},
year = {2013}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1105.3641