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arXiv · 2009.07797

Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions

Chafiq Benhida·Raul E. Curto·George R. Exner
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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. We also consider back-step extensions, subshifts, and completions.

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Chafiq Benhida, Raul E. Curto, George R. Exner. 2020-09-16. Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions. https://doi.org/10.1007/s11785-021-01180-w

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