Multiplication operators on the Bloch space of bounded homogeneous domains

Abstract

In this paper, we study the multiplication operators on the Bloch space of a bounded homogeneous domain in C^n. Specifically, we characterize the bounded and the compact multiplication operators, establish estimates on the operator norm, and determine the spectrum. 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