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Commuting dual Toeplitz operators on weighted Bergman spaces of the unit ball. (English) Zbl 1248.47030

Let \(A^2_{\alpha}(B_n)\) be the standard weighted Bergman space over the unit ball \(B_n\) in \(\mathbb{C}^n\), and let \(P_{\alpha}\) be the corresponding Bergman projection. For a function \(f \in L^{\infty}(B_n)\), the dual Toeplitz operator is defined by \(S_fu = (I-P_{\alpha})(fu)\), for \(u \in (A^2_{\alpha}(B_n))^{\perp}\). The authors study the commutativity, essential commutativity and essential semi-commutativity properties of such dual Toeplitz operators.

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47B47 Commutators, derivations, elementary operators, etc.
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