The Essential Norm of Operators on $A^p_α(\mathbb{B}_n)$

In this paper we characterize the compact operators on $A^p_α(\mathbb{B}_n)$ when $1<p<\infty$ and $α>-1$. The main result shows that an operator on $A^p_α(\mathbb{B}_n)$ is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball.

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