This paper discusses the convexity of the range of the Berezin transform. For a bounded operator T acting on a reproducing kernel Hilbert space H (on a set X), this is the set B(T):={〈Tk?x,k?x〉H:x∈X}, where k?x is the normalized reproducing kernel for H at x∈X. Primarily, we focus on characterizing convexity of this range for a class of composition operators acting on the Hardy space of the unit disk.
NSTL
Elsevier
