English

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 p>0p > 0, the shift is subnormal when every weight (equivalently, every moment) is raised to the pp-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}
}