College of Liberal Arts & Sciences

# Math Physics Seminar - Professor Raúl Curto; Department of Mathematics; The University of Iowa "Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions"

Math Phys - Tuesdays 2:30-3:30 Zoom ID 963 1959 0923

**Professor Raúl Curto**

Department of Mathematics

The University of Iowa

***Title:** "Moment Infinite Divisibility of Weighted Shifts: Sequence Conditions"

**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 they are, under mild conditions, robust under a variety of operations, while 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.

*note - this is continued from the November 10th Operator Theory Seminar