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Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions
Journal article   Peer reviewed

Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions

Chafiq Benhida, Raul E Curto and George R Exner
Complex analysis and operator theory, Vol.16(1), 5
01/01/2022
DOI: 10.1007/s11785-021-01180-w
url
https://arxiv.org/pdf/2009.07797View
Open Access

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.
Mathematics Physical Sciences Mathematics, Applied Science & Technology

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