Summary: Computational Methods and Function Theory
Volume 00 (0000), No. 0, 114 CMFT-MS
Multiplication Operators on the Bloch Space
of Bounded Homogeneous Domains
Robert F. Allen and Flavia Colonna
Abstract. In this paper, we study the multiplication operators on the Bloch
space of a bounded homogeneous domain in Cn
. Specifically, we characterize
the bounded and the compact multiplication operators, establish estimates
on the operator norm, and determine the spectrum. We prove that the only
bounded multiplication operators on the Bloch space of the polydisk are those
whose symbol is constant. Furthermore, we prove that for a large class of
bounded symmetric domains, the isometric multiplication operators are those
whose symbol is a constant of modulus one.
Keywords. Multiplication operators, Bloch space, Homogeneous domains.
2000 MSC. Primary 47B35; Secondary 32A18.
In recent years, the operator theory of many functional Banach spaces that arise
in complex function theory has been studied extensively. Two particular impor-
tant classes of operators are the multiplication operators and the composition