Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions
Functional Analysis
2020-09-17 v1
Abstract
We consider weighted shift operators having the property of moment infinite divisibility; that is, for any , the shift is subnormal when every weight (equivalently, every moment) is raised to the -th power. By reconsidering sequence conditions for the weights or moments of the shift, we obtain a new characterization for such shifts, and we prove that such shifts are, under mild conditions, robust under a variety of operations and also rigid in certain senses. In particular, a weighted shift whose weight sequence has a limit is moment infinitely divisible if and only if its Aluthge transform is. We also consider back-step extensions, subshifts, and completions.
Keywords
Cite
@article{arxiv.2009.07797,
title = {Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions},
author = {Chafiq Benhida and Raul E. Curto and George R. Exner},
journal= {arXiv preprint arXiv:2009.07797},
year = {2020}
}