Computational Methods and Function Theory 9 (2009), No. 2, 679--693
Copyright Heldermann Verlag 2009
Robert F. Allen
allen.rob3@uwlax.edu , University of Wisconsin-La Crosse, Department of Mathematics, La Crosse, WI 54601, U.S.A.
Flavia Colonna
fcolonna@gmu.edu , George Mason University, Department of Mathematical Sciences, Fairfax, VA 22030, U.S.A.
In this paper, we study the multiplication operators on the Bloch space of a bounded homogeneous domain in $\mathbb{C}^n$. 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.
MSC 2000: Primary 47B35; Secondary 32A18.
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