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 ${\mathbb{C}}^n$. 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.

References in corpus (4)

• On the isometric composition operators on the Bloch space in ${\mathbb{C}}^n$
• Isometries and spectra of multiplication operators on the Bloch space
• Weighted Composition Operators between different Bloch-type Spaces in Polydisk
• Weighted Composition Operators from $F(p,q,s)$ to Bloch Type Spaces on the Unit Ball

Cited by in corpus (2)

• Weighted composition operators from $H^{\infty }$ to the Bloch space of a bounded homogeneous domain
• Which multiplication operators are surjective isometries?