Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_α^p$

Details Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_α^p$ Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_α^p$

2011-09-01

arxiv.org/abs/1109.0305v2

Mathematics

Functional Analysis

v1: 36 pages, no figures v2: 36 pages, no figures, typos corrected, submitted

Scientific paper

Let BT be the class of functions $f$ on $\mathbb{C}^n$ where the Berezin transform $B_\alpha (|f|)$ associated to the standard weighted Fock space $F_\alpha ^2$ is bounded, and for $1 < p < \infty$ let $\mathcal{T}_p$ be the norm closure of the algebra generated by Toeplitz operators with BT symbols acting on $F_\alpha ^p$. In this paper, we will show that an operator $A$ is compact on $F_\alpha ^p$ if and only if $A \in \mathcal{T}_p$ and the Berezin transform $B_\alpha (A)$ of $A$ vanishes at infinity.

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