 
Summary: ON NORMS OF COMPOSITION OPERATORS ON HARDY
SPACES
P. AVRAMIDOU AND F. JAFARI
Abstract. The computation of the norm of composition operators on Hardy
spaces is very hard, even for choice of fairly simple symbol maps. In this pa
per, we shall give an approach comparing the norm of these operators with
the spectral radius, the action of the operators and their adjoints on the re
producing kernel functions. Our goal is to characterize, as full as possible, the
behavior of these four quantities with respect to the fixed points of the induc
ing maps of composition operators. This paper extends the work of Appell,
Bourdon and Thrall and goes a long way at answering an open question of
Cowen and MacCluer.
1. Introduction
Let be an analytic map of the unit disk, D, into itself, and C defined by
Cf = f
denote the composition operator induced by on the Hardy space H2
(D). It is
well known that C is a bounded operator; however, with the exception of a few
classes of functions the exact value of the norm of these basic operators are hard
to calculate.
