Dual Toeplitz Operators on the Sphere Via Spherical Isometries

Abstract

We solve a characterization problem for dual Hardy-space Toeplitz operators on the unit sphere \({\mathbb{S}_{n}}\) in \({\mathbb{C}^{n}}\) posed by Guediri (Acta Math Sin (English series) 29(9):1791–1808, 2013). Our proof relies on the observation that dual Toeplitz operators on the orthogonal complement \({H^{2}(\mathbb{S}_{n})^{\bot}}\) of the Hardy space in L2 can be viewed as Toeplitz operators with respect to a suitable spherical isometry. This correspondence also allows us to determine the commutator ideal of the dual Toeplitz C*-algebra.