Multiplication Operators on the Bloch Space of Bounded Homogeneous Domains

被引：0
作者：
Robert F. Allen
Flavia Colonna
机构：
[1] University of Wisconsin-La Crosse,Department of Mathematics
[2] George Mason University,Department of Mathematical Sciences
来源：
Computational Methods and Function Theory | 2009年 / 9卷 / 2期
关键词：
Multiplication operators; Bloch space; homogeneous domains; Primary 47B35; Secondary 32A18;
D O I：
10.1007/BF03321751
中图分类号：
学科分类号：
摘要：
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.
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页码：679 / 693
页数：14
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