Abstract. Operators of type $f\to f\circ \varphi $ acting on function spaces are called composition operators. We consider composition operators acting on the Hilbert Hardy space on the open unit disc or the right half-plane, study when they are similar to contractions, and obtain results interesting from the point of view of dilation theory of contractions and function theory.
AMS Subject Classification
(1991): 47B33, 47A45
Received August 24, 2018 and in final form December 14, 2018. (Registered under 78/2018.)