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

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

2012-04-25

arxiv.org/abs/1204.5548v1

Mathematics

Classical Analysis and ODEs

v1: 32 pages

Scientific paper

It this paper we characterize the compact operators on
$A^p_\alpha(\mathbb{B}_n)$ when $1-1$. The main result
shows that an operator on $A^p_\alpha(\mathbb{B}_n)$ is compact if and only if
its Berezin transform vanishes on the boundary of the ball and additionally
this operator belongs to the Toeplitz algebra $\mathcal{T}_{p,\alpha}$.

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