Journal article
Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions
Complex analysis and operator theory, Vol.16(1), 5
01/01/2022
DOI: 10.1007/s11785-021-01180-w
Abstract
We consider weighted shift operators having the property of moment infinite divisibility; that is, for any p > 0, the shift is subnormal when every weight (equivalently, every moment) is raised to the p-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. As a consequence, we prove that the Aluthge transform maps the class of moment infinitely divisible weighted shifts bijectively onto itself. We also consider back-step extensions, subshifts, and completions.
Details
- Title: Subtitle
- Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions
- Creators
- Chafiq Benhida - Univ Sci & Technol Lille, UFR Math, F-59655 Villeneuve Dascq, FranceRaul E Curto - Univ Iowa, Dept Math, Iowa City, IA 52242 USAGeorge R Exner - Bucknell University
- Resource Type
- Journal article
- Publication Details
- Complex analysis and operator theory, Vol.16(1), 5
- DOI
- 10.1007/s11785-021-01180-w
- ISSN
- 1661-8254
- eISSN
- 1661-8262
- Publisher
- SPRINGER BASEL AG
- Number of pages
- 23
- Language
- English
- Date published
- 01/01/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984240772502771
Metrics
17 Record Views