Compactness characterization of operators in the Toeplitz algebra of the Fock space F-alpha(p)

Abstract

For 1 < p < infinity let T-p(alpha) be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space F-alpha(p). In this paper, we will show that an operator A is compact on F-alpha(p) and only if A is an element of T-p(alpha) and the Berezin transform B-alpha(A) of A vanishes at infinity. (C) 2012 Elsevier Inc. All rights reserved.