Operator Theory Seminar

April 17, 2018 - 1:30pm
309 VAN

"Subnormality of Shifts Related to Composition Operators: Do the Shifts Remember X/yarphi$? by George Exner, Ph.D., Department of Mathematics, Bucknell University

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).