Recursiveness for commutative and noncommutative moment problems on directed trees

Ed White

In this talk, we first recall the notion of hyponormality, subnormality, and recursion for moment problems on 2-variable weighted shifts (2VWS). We then outline the construction of the noncommutative moment matrix and use it to define recursion for a weighted shift on a full binary tree with root. This construction also gives us a representation for the moments as well as a characterization for subnormality from this representation. We then outline the procedure for turning a 2VWS into weighted shifts on a full binary tree with root and prove that hyponormality, subnormality, and recursive relations are all maintained under this construction. Finally, we outline the procedure for turning a weighted shift on a directed tree with root into a 2VWS and show that hyponormality and subnormality may not be maintained.

To participate in this event virtually via Zoom, go to https://uiowa.zoom.us/j/95316149275.