#### Title

Moment Infinitely Divisible Weighted Shifts

#### Publication Date

2019

#### Description

We say that a weighted shift Wα with (positive) weight sequence α : α0, α1,... is moment infinitely divisible (MID) if, for every t > 0, the shift with weight sequence αt : αt 0, αt 1,... is subnormal. Assume that Wα is a contraction, i.e., 0 < αi ≤ 1 for all i ≥ 0. We show that such a shift Wα is MID if and only if the sequence α is log completely alternating. This enables the recapture or improvement of some previous results proved rather differently. We derive in particular new conditions sufficient for subnormality of a weighted shift, and each example contains implicitly an example or family of infinitely divisible Hankel matrices, many of which appear to be new.

#### Journal

Complex Analysis and Operator Theory

#### Volume

13

#### Issue

1

#### First Page

241

#### Last Page

255

#### Department

Mathematics

#### DOI

https://doi.org/10.1007/s11785-018-0771-z

#### Recommended Citation

Curto, Raúl E.; Benhida, Chafiq; and Exner, George R.. "Moment Infinitely Divisible Weighted Shifts." *Complex Analysis and Operator Theory* (2019)
: 241-255.