Operator Theory Seminar

Speaker: 
George Exner, Bucknell University
Topic: 
"Subnormality of shifts related to composition operators: do the shifts remember $\varphi$?"

Abstract:
We consider composition operators $C_\varphi$ on $H^2$ induced by certain linear fractional transformations $\varphi$ mapping $\mathbb{D}$ into itself with the assumption that the Denjoy-Wolff point is $1$.  Certain restrictions of $C_\varphi^*$, arising from iterates under $\varphi$ of some point $z$ in the disk, are similar to weighted shifts.  The subnormality or hyponormality of the shift carries information about the (other) fixed point of $\varphi$ and the iteration point $z$ in pleasing geometrical ways (joint work with I. Chalendar).

Event Date: 
April 17, 2018 - 1:30pm to 2:30pm
Location: 
309 VAN
Calendar Category: 
Seminar