Symmetries and reflections from composition operators in the disk

Esteban Andruchow, Gustavo Corach, Lázaro Recht

We study the composition operators $C_a$ acting on the Hardy space $H^2$ of the unit disk, given by $C_{a}f=f\circ \ddot{I}{†}_a$, where $$\ddot{I}{†}_a(z)=\frac{a-z}{1-\bar{a}z},$$ for $|a|<1$. Thes…