2020/09/16 by Benhida, Chafiq, Curto, Raul E., Exner, George R.
#47 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2009.07797
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.