Compactness characterization of operators in the Toeplitz algebra of the Fock space Fαp

摘要

For 1<∞ let T _p ~α be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space F _α ~p In this paper, we will show that an operator A is compact on Fαp if and only if A∈T _p ~α and the Berezin transform B _α(A) of A vanishes at infinity.