Toeplitz Operators on the Fock Space

By Joshua Isralowitz, Kehe Zhu. 2010

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Hankel Operators on Fock Spaces and Related Bergman Kernel Estimates (2010, background): “Note that [12] also treats Schatten class membership of Toeplitz operators for p < 1.”
Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_\alpha ^p$ (2011, background): “(w) = es 2 |z 2/4α. Proof. See [7]. Lemma 2.4. For any r,α,p>0, any z∈ Cn, and any entire f, there exists Cindependent of fand zwhere f(z)e−α2 |z 2 p ≤ C Z B(z,r) f(w)e−α2 |w 2 p dv(w). Proof. See [16]. For the rest of the paper, we will canonically treat Z2n as a lattice in Cn. The following is ”
Toeplitz Operators from One Fock Space to Another (2011, background): “Given λ = {λk }∈ l p , define f (w )= � ∞=1 |λk|χB(ak,r)(w). Lemma 2.1 of [ 11 ]”