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

November 17, 2020 - 2:30pm to 3:30pm
via Zoom

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