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Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_α^p$ (1109.0305v3)

Published 1 Sep 2011 in math.FA and math.CV

Abstract: For $1 < p < \infty$ let $\mathcal{T}p \alpha$ 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 $F_\alpha p$ if and only if $A \in \mathcal{T}p \alpha$ and the Berezin transform $B\alpha (A)$ of $A$ vanishes at infinity.

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