Bulletin of the Australian Mathematical Society

Table of Contents - October 2000 - Volume 62, Issue 02  

Research Article

Toeplitz operators on the Bergman space of the unit ball

Roberto Raimondoa1

a1 Department of Economics, University of California at Berkeley, Evans Hall, Berkeley, CA 94720, United States of America, e-mail: raimondo@econ.berkeley.edu

Abstract

We prove that if an operator A is a finite sum of finite products of Toeplitz operators on the Bergman space of the unit ball Bn, then A is compact if and only if its Berezin transform vanishes at the boundary. For n = 1 the result was obtained by Axler and Zheng in 1997.

(Received January 10 2000)