The Essential Norm of Operators on Ap α(Bn) - Mitkovski, Mishko (2013)
In this paper we characterize the compact operators on the weighted Bergman spaces Ap α(Bn) when 1 <p< ∞ and α > −1. The main result shows that an operator on Ap α(Bn) is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball