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Summary: Weighted Composition Operators on the Bloch
Space of a Bounded Homogeneous Domain
Robert F. Allen and Flavia Colonna
In honor of Israel Gohberg on the occasion of his 80th birthday.
Abstract. In this paper, we present the current results in the study of weighted
composition operators on the Bloch space of bounded homogeneous domains
in Cn
with particular emphasis on the issues of boundedness and compactness.
We also discuss the bounded and the compact weighted composition operators
from the Bloch space to the Hardy space H
.
Mathematics Subject Classification (2000). 47B38, 32A18, 30D45.
Keywords. Weighted composition operators, Bloch space, Homogeneous do-
mains.
1. Introduction
Let X be a Banach space of holomorphic functions on a domain Cn
. For a
holomorphic function on and a holomorphic self-map of , the linear operator
defined by
W,(f) = (f ), f X,
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